关于斜拉桥的中英文翻译学士学位论文
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桥梁工程中英文对照外文翻译文献BRIDGE ENGINEERING AND AESTHETICSEvolvement of bridge Engineering,brief reviewAmong the early documented reviews of construction materials and structu re types are the books of Marcus Vitruvios Pollio in the first century B.C.The basic principles of statics were developed by the Greeks , and were exemplifi ed in works and applications by Leonardo da Vinci,Cardeno,and Galileo.In the fifteenth and sixteenth century, engineers seemed to be unaware of this record , and relied solely on experience and tradition for building bridges and aqueduc ts .The state of the art changed rapidly toward the end of the seventeenth cent ury when Leibnitz, Newton, and Bernoulli introduced mathematical formulatio ns. Published works by Lahire (1695)and Belidor (1792) about the theoretical a nalysis of structures provided the basis in the field of mechanics of materials .Kuzmanovic(1977) focuses on stone and wood as the first bridge-building materials. Iron was introduced during the transitional period from wood to steel .According to recent records , concrete was used in France as early as 1840 for a bridge 39 feet (12 m) long to span the Garoyne Canal at Grisoles, but r einforced concrete was not introduced in bridge construction until the beginnin g of this century . Prestressed concrete was first used in 1927.Stone bridges of the arch type (integrated superstructure and substructure) were constructed in Rome and other European cities in the middle ages . Thes e arches were half-circular , with flat arches beginning to dominate bridge wor k during the Renaissance period. This concept was markedly improved at the e nd of the eighteenth century and found structurally adequate to accommodate f uture railroad loads . In terms of analysis and use of materials , stone bridgeshave not changed much ,but the theoretical treatment was improved by introd ucing the pressure-line concept in the early 1670s(Lahire, 1695) . The arch the ory was documented in model tests where typical failure modes were considere d (Frezier,1739).Culmann(1851) introduced the elastic center method for fixed-e nd arches, and showed that three redundant parameters can be found by the us e of three equations of coMPatibility.Wooden trusses were used in bridges during the sixteenth century when P alladio built triangular frames for bridge spans 10 feet long . This effort also f ocused on the three basic principles og bridge design : convenience(serviceabili ty) ,appearance , and endurance(strength) . several timber truss bridges were co nstructed in western Europe beginning in the 1750s with spans up to 200 feet (61m) supported on stone substructures .Significant progress was possible in t he United States and Russia during the nineteenth century ,prompted by the ne ed to cross major rivers and by an abundance of suitable timber . Favorable e conomic considerations included initial low cost and fast construction .The transition from wooden bridges to steel types probably did not begin until about 1840 ,although the first documented use of iron in bridges was the chain bridge built in 1734 across the Oder River in Prussia . The first truss completely made of iron was in 1840 in the United States , followed by Eng land in 1845 , Germany in 1853 , and Russia in 1857 . In 1840 , the first ir on arch truss bridge was built across the Erie Canal at Utica .The Impetus of AnalysisThe theory of structures ,developed mainly in the ninetheenth century,foc used on truss analysis, with the first book on bridges written in 1811. The Wa rren triangular truss was introduced in 1846 , supplemented by a method for c alculating the correcet forces .I-beams fabricated from plates became popular in England and were used in short-span bridges.In 1866, Culmann explained the principles of cantilever truss bridges, an d one year later the first cantilever bridge was built across the Main River in Hassfurt, Germany, with a center span of 425 feet (130m) . The first cantilever bridge in the United States was built in 1875 across the Kentucky River.A most impressive railway cantilever bridge in the nineteenth century was the Fir st of Forth bridge , built between 1883 and 1893 , with span magnitudes of 1 711 feet (521.5m).At about the same time , structural steel was introduced as a prime mater ial in bridge work , although its quality was often poor . Several early exampl es are the Eads bridge in St.Louis ; the Brooklyn bridge in New York ; and t he Glasgow bridge in Missouri , all completed between 1874 and 1883.Among the analytical and design progress to be mentioned are the contrib utions of Maxwell , particularly for certain statically indeterminate trusses ; the books by Cremona (1872) on graphical statics; the force method redefined by Mohr; and the works by Clapeyron who introduced the three-moment equation s.The Impetus of New MaterialsSince the beginning of the twentieth century , concrete has taken its place as one of the most useful and important structural materials . Because of the coMParative ease with which it can be molded into any desired shape , its st ructural uses are almost unlimited . Wherever Portland cement and suitable agg regates are available , it can replace other materials for certain types of structu res, such as bridge substructure and foundation elements .In addition , the introduction of reinforced concrete in multispan frames at the beginning of this century imposed new analytical requirements . Structures of a high order of redundancy could not be analyzed with the classical metho ds of the nineteenth century .The importance of joint rotation was already dem onstrated by Manderla (1880) and Bendixen (1914) , who developed relationshi ps between joint moments and angular rotations from which the unknown mom ents can be obtained ,the so called slope-deflection method .More simplification s in frame analysis were made possible by the work of Calisev (1923) , who used successive approximations to reduce the system of equations to one simpl e expression for each iteration step . This approach was further refined and integrated by Cross (1930) in what is known as the method of moment distributi on .One of the most import important recent developments in the area of anal ytical procedures is the extension of design to cover the elastic-plastic range , also known as load factor or ultimate design. Plastic analysis was introduced with some practical observations by Tresca (1846) ; and was formulated by Sa int-Venant (1870) , The concept of plasticity attracted researchers and engineers after World War Ⅰ, mainly in Germany , with the center of activity shifting to England and the United States after World War Ⅱ.The probabilistic approa ch is a new design concept that is expected to replace the classical determinist ic methodology.A main step forward was the 1969 addition of the Federal Highway Adim inistration (FHWA)”Criteria for Reinforced Concrete Bridge Members “ that co vers strength and serviceability at ultimate design . This was prepared for use in conjunction with the 1969 American Association of State Highway Offficials (AASHO) Standard Specification, and was presented in a format that is readil y adaptable to the development of ultimate design specifications .According to this document , the proportioning of reinforced concrete members ( including c olumns ) may be limited by various stages of behavior : elastic , cracked , an d ultimate . Design axial loads , or design shears . Structural capacity is the r eaction phase , and all calculated modified strength values derived from theoret ical strengths are the capacity values , such as moment capacity ,axial load ca pacity ,or shear capacity .At serviceability states , investigations may also be n ecessary for deflections , maximum crack width , and fatigue .Bridge TypesA notable bridge type is the suspension bridge , with the first example bu ilt in the United States in 1796. Problems of dynamic stability were investigate d after the Tacoma bridge collapse , and this work led to significant theoretica l contributions Steinman ( 1929 ) summarizes about 250 suspension bridges bu ilt throughout the world between 1741 and 1928 .With the introduction of the interstate system and the need to provide stru ctures at grade separations , certain bridge types have taken a strong place in bridge practice. These include concrete superstructures (slab ,T-beams,concrete b ox girders ), steel beam and plate girders , steel box girders , composite const ruction , orthotropic plates , segmental construction , curved girders ,and cable-stayed bridges . Prefabricated members are given serious consideration , while interest in box sections remains strong .Bridge Appearance and AestheticsGrimm ( 1975 ) documents the first recorded legislative effort to control t he appearance of the built environment . This occurred in 1647 when the Cou ncil of New Amsterdam appointed three officials . In 1954 , the Supreme Cou rt of the United States held that it is within the power of the legislature to de termine that communities should be attractive as well as healthy , spacious as well as clean , and balanced as well as patrolled . The Environmental Policy Act of 1969 directs all agencies of the federal government to identify and dev elop methods and procedures to ensure that presently unquantified environmenta l amentities and values are given appropriate consideration in decision making along with economic and technical aspects .Although in many civil engineering works aesthetics has been practiced al most intuitively , particularly in the past , bridge engineers have not ignored o r neglected the aesthetic disciplines .Recent research on the subject appears to lead to a rationalized aesthetic design methodology (Grimm and Preiser , 1976 ) .Work has been done on the aesthetics of color ,light ,texture , shape , and proportions , as well as other perceptual modalities , and this direction is bot h theoretically and empirically oriented .Aesthetic control mechanisms are commonly integrated into the land-use re gulations and design standards . In addition to concern for aesthetics at the sta te level , federal concern focuses also on the effects of man-constructed enviro nment on human life , with guidelines and criteria directed toward improving quality and appearance in the design process . Good potential for the upgrading of aesthetic quality in bridge superstructures and substructures can be seen in the evaluation structure types aimed at improving overall appearance .Lords and lording groupsThe loads to be considered in the design of substructures and bridge foun dations include loads and forces transmitted from the superstructure, and those acting directly on the substructure and foundation .AASHTO loads . Section 3 of AASHTO specifications summarizes the loa ds and forces to be considered in the design of bridges (superstructure and sub structure ) . Briefly , these are dead load ,live load , iMPact or dynamic effec t of live load , wind load , and other forces such as longitudinal forces , cent rifugal force ,thermal forces , earth pressure , buoyancy , shrinkage and long t erm creep , rib shortening , erection stresses , ice and current pressure , collisi on force , and earthquake stresses .Besides these conventional loads that are ge nerally quantified , AASHTO also recognizes indirect load effects such as fricti on at expansion bearings and stresses associated with differential settlement of bridge components .The LRFD specifications divide loads into two distinct cate gories : permanent and transient .Permanent loadsDead Load : this includes the weight DC of all bridge components , appu rtenances and utilities, wearing surface DW nd future overlays , and earth fill EV. Both AASHTO and LRFD specifications give tables summarizing the unit weights of materials commonly used in bridge work .Transient LoadsVehicular Live Load (LL) Vehicle loading for short-span bridges :considera ble effort has been made in the United States and Canada to develop a live lo ad model that can represent the highway loading more realistically than the H or the HS AASHTO models . The current AASHTO model is still the applica ble loading.桥梁工程和桥梁美学桥梁工程的发展概况早在公元前1世纪,Marcus Vitrucios Pollio 的著作中就有关于建筑材料和结构类型的记载和评述。
摘要XX大桥主孔斜拉桥是一座公铁两用的斜拉桥,跨度为504米。
是国内首座上层为六车道公路桥面,下层为四线铁路的斜拉桥。
本文以该斜拉桥为工程背景。
首先采用SAP90程序,建立全桥三维有限元模型,考虑了主桁、主塔和斜拉索的关系。
三片桁架通过横梁联系,将混凝土桥面板、钢桥面板按恒载考虑。
进行恒活载计算时,将横纵梁、桥面板、道碴、道碴槽、汽车活载、列车活载等转化为集中力施加到桁架节点上。
并以刚度控制为标准确定斜拉索初张力。
在恒活载内力分析中,上层公路桥面用弹性支撑连续梁法,下层铁路桥面用杠杆法计算横向分布系数,从而确定中桁为最不利桁架。
结构计算以跨中和支座处的断面为控制断面,绘出控制杆件的轴力影响线,利用影响线加活载并求内力。
按照公路规范进行内力组合,对控制杆件进行强度、刚度和疲劳强度的检算。
最后进行结构性能评定。
关键词:斜拉桥,钢桁梁,初张力,内力分析,结构验算ABSTRACTThe main span of Tianxingzhou Bridge is a Cable-stayed Bridge in Wuhan, which is used for highway and railway. The main span is 504m.It is the first bridge that its up layer can hold 6 lanes of highway, and it’s down layer is used for 4 track railway in our country.The thesis takes this Cable-stayed Bridge for engineering background.First, three dimensional finite element model is set up using SAP90 program.Consider revising the connection of primary truss, main tower and cables,regarding concrete deck and steel deck as dead load.The three trusses are integrated through cross beams. In the process of load calculating, the gravity of cross beams, girders, deck, ballast, ballast trough are transformed into concentrated force which compel on the joints of trusses.Moreover, according to the stiffness norm, the initial prestress are added to the cables.In the process of internal force analysis, the middle truss is determined as the most dangerous truss through calculating cross subsection factor. The up layer adopts the method of continuous beams on elastic support,and the down layer use heaver method.Next, definite the most dangerous section, the influence line of the most dangerous member is made , and calculate the internal force.According to the highway bridge standard and railway, combine internal force.Check the strength, rigidity and fatigue initiation of the control member.Last, the structural performance is evaluated.Key words: Cable-stayed Bridge, steel truss girder, initial prestress, internal force analysis, structural check。
矮塔斜拉桥起源于法国,兴起于日本,在国内近20年有较大的发展。
它具有与连续刚构极为相似的受力特点,即矮塔斜拉桥的斜拉索就相当于把连续刚构梁的体内的预应力转移到矮塔斜拉桥的桥塔上,索鞍相当于体外预应力索的转折点,因此它同时兼有斜拉桥和连续刚构的结构特点,当桥梁跨径在100~200m的范围里,该类桥型具有很强的竞争力。
已建的矮塔斜拉桥大都采用贯通式锚固方式,贯通锚固之前一般用双套管鞍座结构,但双套管结构由于易产生应力集中、换索不方便等缺点逐渐被分丝管结构所取代。
分丝管内部构造极为复杂,分丝管把索力传递给鞍座,之后鞍座又与混凝土发生高度非线性的接触问题,其受力较为复杂。
本文以某矮塔斜拉桥桥为依托,在大量调研的基础上,利用结构有限元的方法,对索塔锚固区(分丝管索鞍结构)局部应力分布情况进行分析。
主要内容包括:1、对常规斜拉桥与矮塔斜拉桥在索塔、主梁、斜拉索的构造以及结构体系进行了总结和比对;2、应用空间有限元软件Madis Civil对该大桥进行了全桥静力分析;3、应用大型有限元软件ABAQUS和FEA对该大桥索塔锚固区进行基于接触理论的混凝土局部应力分析,得出分丝管应力分布规律,为同类桥型设计和施工提供参考。
Extra-dosed cable-stayed bridge originated in France, thrived in Japan and greatly developed in China in recent 20 years. It has similar loading features as continuous rigid frame bridge. The stayed-cable of extra-dosed cable-stayed bridge is the equivalent of transferring the body prestress of the continuous rigid frame bridge onto the tower of extra-dosed cable-stayed bridge. The cable saddle equals to turning point of the external prestressing cables, therefore it has structure characteristics of both the cable-stayed bridge and continuous rigid frame bridge. It has strong competitiveness when the bridge spans in the range of 100 ~ 200 m.Most built extra-dosed cable-stayed bridge use drive-through type anchorage. We often use double pipe saddle before drive-through anchoring. However, the double-pipe saddle is gradually replaced by devillicate structure because of its defect of easily producing stress concentration and inconvenience of cable replacement. The internal structure of devillicate pipe is quite complicated. The devillicate pipe passes the cable force to saddle and the saddle will has highly nonlinear contact with the concrete, the force is relatively complicated. This paper is on basis of certain extra-dosed cable stayed bridge and supported by a large quantity of research, use the method of structure finite element to analyze partial stress distribution in bridge tower anchorage zone ( devillicate pipe saddle structure). The main contents include:1.Make conclusion and comparison between conventional cable-stayed bridge and extra-dosed cable-stayed bridge in saddle, main bean, cable formation and structural system;2. Use space finite element software Madis Civil to make analysis on bridge static;3. Use large finite element software ABAQUS and FEA to make analysis on contact theory based concrete partial stress in bridge tower anchorage zone. Reach the law of devillicate pipe stress distribution and provide a reference for similar bridge design and construction.。
附录1 英文文献翻译斜拉桥斜拉桥特别适合于200m~500m的跨径范围,可以说是从连续箱梁桥到加劲悬索桥的过渡。
它起源于战后德国,当时主要是为了节约刚材。
高强钢材的应用,先进的焊接技术和电子计算机对高度超静定结构的严密分析,极大地促进了斜拉桥的发展。
斜拉桥的主要承载构件是:斜拉索、索塔和正交异性板。
简而言之,锚固于桥面板和塔上的斜拉索取消了中间桥墩,因而为航行提供了更大的桥下净宽。
桥面板通过斜拉索以扇形(集中于塔顶)或琴形(多点锚于塔)来形成对桥面板的多点支承。
密索体系减小了桥面板支承点之间的距离,并减小了结构高度,这样设计和张拉的拉索使结构的工作行为类似于刚性支承的连续梁。
由于斜拉索的阻尼作用,斜拉桥的桥面板不致像悬索桥那样容易风致摆动。
拉索可以像诺德利贝桥那样设置成单索面,可以像斯特伦松德桥或杜塞尔多夫桥那样设置成垂直双索面,也可以像塞韦林桥设置成双斜索面。
单索面体系的优点是:桥面板上的锚固区分布于交通中线上,使桥面总宽度最小。
对于双索面体系,则需要额外的桥面宽度来调节塔梁的锚固。
从美学上看,单索面体系更吸引人,因为这为两侧的司机提供了更广阔的视野。
对双索面而言,桥梁一侧的拉索会给人以交叉的感觉。
双斜索面体系,像塞韦林桥一样索从A型框架的顶尖辐射下来,使上部结构具有三维结构的性能,减小了风引起的桥面板扭振。
对单索面体系,偏心集中荷载引起的扭矩使箱形截面正交异性板的应用成为必要。
双索面体系的桥面板一般是正交异性的箱梁,也可以是预应力混凝土梁,如委内瑞拉的马拉开波桥和西德美因河上的赫希斯特桥。
拉索是预张拉的锁丝结构,这些索不易腐蚀,抗拉性强。
最后一个特点对斜拉桥是重要的,因为伸长会引起更大的弯矩和增加结构高度。
斜拉索的倾角会影响塔的高度。
塔为锚固索而在锚固点以上增加高度是正常的,就像诺德利贝桥(这种情况下,作为城市的礼物)。
不仅要考虑结构,在塔形的选择中,美学也占有突出的地位。
例如,由于塞韦林桥接近科洛涅大教堂,故采用A型框架。
中英文对照外文翻译文献(文档含英文原文和中文翻译)Recent Research and Design Developments in Steel and Composite Steel-concrete Structures in USAThe paper will conclude with a look toward the future of structural steel research.1. Research on steel bridgesThe American Association of State Transportation and Highway Officials (AASTHO) is the authority that promulgates design standards for bridges in the US. In 1994 it has issued a new design specification which is a Limit States Design standard that is based on the principles of reliability theory. A great deal of work went into the development of this code in the past decade, especially on calibration and on the probabilistic evaluation of the previous specification. The code is now being implemented in the design office, together with the introduction of the SystemeInternationale units. Many questions remain open about the new method of design, and there are many new projects that deal with the reliability studies of the bridge as a system. One such current project is a study to develop probabilistic models, load factors, and rational load-combination rules for the combined effects of live-load and wind; live-load and earthquake; live-load, wind and ship collision; and ship collision, wind, and scour. There are also many field measurements of bridge behavior, using modern tools of inspection and monitoring such as acoustic emission techniques and other means of non-destructive evaluation. Such fieldwork necessitates parallel studies in the laboratory, and the evolution of ever more sophisticated high-technology data transmission methods.America has an aging steel bridge population and many problems arise from fatigue and corrosion. Fatigue studies on full-scale components of the Williamsburg Bridge in New York have recently been completed at Lehigh University. A probabilistic AASTHO bridge evaluation regulation has been in effect since 1989, and it is employed to assess the future useful life of structures using rational methods that include field observation and measurement together with probabilistic analysis. Such an activity also fosters additional research because many issues are still unresolved. One such area is the study of the shakedown of shear connectors in composite bridges. This work has been recently completed at the University of Missouri.In addition to fatigue and corrosion, the major danger to bridges is the possibility of earthquake induced damage. This also has spawned many research projects on the repair and retrofit of steel superstructures and the supporting concrete piers. Many bridges in the country are being strengthened for earthquake resistance. One area that is receiving much research attention is the strengthening of concrete piers by "jacketing" them by sheets of high-performance reinforced plastic.The previously described research deals mainly with the behavior of existing structures and the design of new bridges. However, there is also a vigorous activity on novel bridge systems. This research is centered on the application of high-performance steels for the design of innovative plate and box-girder bridges, such as corrugated webs, combinations of open and closed shapes, and longer spansfor truss bridges. It should be mentioned here that, in addition to work on steel bridges, there is also very active research going on in the study of the behavior of prestressed concrete girders made from very high strength concrete. The performance and design of smaller bridges using pultruded high-performance plastic composite members is also being studied extensively at present. New continuous bridge systems with steel concrete composite segments in both the positive moment and the negative moment regions are being considered. Several researchers have developed strong capabilities to model the three-dimensional non-linear behavior of individual plate girders, and many studies are being performed on the buckling and post-buckling characteristics of such panion experimental studies are also made,especially on members built from high-performance steels. A full-scale bridge of such steel has been designed, and will soon be constructed and then tested under traffic loading. Research efforts are also underway on the study of the fatigue of large expansion joint elements and on the fatigue of highway sign structures.The final subject to be mentioned is the resurgence of studies of composite steel concrete horizontally curved steel girder bridges. A just completed project at the University of Minnesota monitored the stresses and the deflections in a skewed and curved bridge during all phases of construction, starting from the fabrication yard to the completed bridge.~ Excellent correlation was found to exist between the measured stresses and deformations and the calculated values. The stresses and deflections during construction were found to be relatively small, that is, the construction process did not cause severe trauma to the system. The bridge has now been tested under service loading, using fully loaded gravel trucks, for two years, and it will continue to be studied for further years to measure changes in performance under service over time. A major testing project is being conducted at the Federal Highway Administration laboratory in Washington, DC, where a half-scale curved composite girder bridge is currently being tested to determine its limit states. The test-bridge was designed to act as its own test-frame, where various portions can be replaced after testing. Multiple flexure tests, shear tests, and tests under combined bending and shear, are thus performed with realistic end-conditions and restraints. The experiments arealso modeled by finite element analysis to check conformance between reality and prediction. Finally design standards will be evolved from the knowledge gained. This last project is the largest bridge research project in the USA at the present time.From the discussion above it can be seen that even though there is no large expansion of the nation's highway and railroad system, there is extensive work going on in bridge research. The major challenge facing both the researcher and the transportation engineer is the maintenance of a healthy but aging system, seeing to its gradual replacement while keeping it safe and serviceable.2. Research on steel members and framesThere are many research studies on the strength and behavior of steel building structures. The most important of these have to do with the behavior and design of steel structures under severe seismic events. This topic will be discussed later in this paper. The most significant trends of the non-seismic research are the following: "Advanced" methods of structural analysis and design are actively studied at many Universities, notably at Cornell, Purdue, Stanford, and Georgia Tech Universities. Such analysis methods are meant to determine the load-deformation behavior of frames up to and beyond failure, including inelastic behavior, force redistribution, plastic hinge formation, second-order effects and frame instability. When these methods are fully operational, the structure will not have to undergo a member check, because the finite element analysis of the frame automatically performs this job. In addition to the research on the best approaches to do this advanced analysis, there are also many studies on simplifications that can be easily utilized in the design office while still maintaining the advantages of a more complex analysis. The advanced analysis method is well developed for in-plane behavior, but much work is yet to be done on the cases where bi-axial bending or lateraltorsional buckling must be considered. Some successes have been achieved, but the research is far from complete.Another aspect of the frame behavior work is the study of the frames with semirigid joints. The American Institute of Steel Construction (AISC) has published design methods for office use. Current research is concentrating on the behavior ofsuch structures under seismic loading. It appears that it is possible to use such frames in some seismic situations, that is, frames under about 8 to 10 stories in height under moderate earthquake loads. The future of structures with semi-rigid frames looks very promising, mainly because of the efforts of researchers such as Leon at Georgia Tech University, and many others.Research on member behavior is concerned with studying the buckling and post buckling behavior of compact angle and wide-flange beam members by advanced commercial finite element programs. Such research is going back to examine the assumptions made in the 1950s and 1960s when the plastic design compactness and bracing requirements were first formulated on a semi-empirical basis. The non-linear finite element computations permit the "re-testing" of the old experiments and the performing of new computer experiments to study new types of members and new types of steels. White of Georgia Tech is one of the pioneers in this work. Some current research at the US military Academy and at the University of Minnesota by Earls is discussed later in this report. The significance of this type of research is that the phenomena of extreme yielding and distortion can be efficiently examined in parameter studies performed on the computer. The computer results can be verified with old experiments, or a small number of new experiments. These studies show a good prospect fornew insights into old problems that heretofore were never fully solved.3. Research on cold-formed steel structuresNext to seismic work, the most active part of research in the US is on cold-formed steel structures. The reason for this is that the supporting industry is expanding, especially in the area of individual family dwellings. As the cost of wood goes up, steel framed houses become more and more economical. The intellectual problems of thin-walled structures buckling in multiple modes under very large deformations have attracted some of the best minds in stability research. As a consequence, many new problems have been solved: complex member stiffening systems, stability and bracing of C and Z beams, composite slabs, perforated columns, standing-seam roof systems, bracing and stability of beams with very complicatedshapes, cold-formed members with steels of high yield stress-to-tensile strength ratio, and many other interesting applications. The American Iron and Steel Institute (AISI) has issued a new expanded standard in 1996 that brought many of these research results into the hands of the designer.4. Research on steel-concrete composite structuresAlmost all structural steel bridges and buildings in the US are built with composite beams or girders. In contrast, very few columns are built as composite members. The area of composite Column research is very active presently to fill up the gap of technical information on the behavior of such members. The subject of steel tubes filled with high-strength concrete is especially active. One of the aims of research performed by Hajjar at the University of Minnesota is to develop a fundamental understanding of the various interacting phenomena that occur in concrete-filled columns and beam-columns under monotonic and cyclic load. The other aim is to obtain a basic understanding of the behavior of connections of wide-flange beams to concrete filled tubes.Other major research work concerns the behavior and design of built-up composite wide-flange bridge girders under both positive and negative bending. This work is performed by Frank at the University of Texas at Austin and by White of Georgia Tech, and it involves extensive studies of the buckling and post-buckling of thin stiffened webs. Already mentioned is the examination of the shakedown of composite bridges. The question to be answered is whether a composite bridge girder loses composite action under repeated cycles of loads which are greater than the elastic limit load and less than the plastic mechanism load. A new study has been initiated at the University of Minnesota on the interaction between a semi-rigid steel frame system and a concrete shear wall connected by stud shear connectors.5. Research on connectionsConnection research continues to interest researchers because of the great variety of joint types. The majority of the connection work is currently related to the seismic problems that will be discussed in the next section of this paper. The most interest in non-seismic connections is the characterization of the monotonic moment-rotationbehavior of various types of semi-rigid joints.6. Research on structures and connections subject to seismic forcesThe most compelling driving force for the present structural steel research effort in the US was the January 17, 1994 earthquake in Northridge, California, North of Los Angeles. The major problem for steel structures was the extensive failure of prequalified welded rigid joints by brittle fracture. In over 150 buildings of one to 26 stories high there were over a thousand fractured joints. The buildings did not collapse, nor did they show any external signs of distress, and there were no human injuries or deaths. A typical joint is shown in Fig. 2.2.1.In this connection the flanges of the beams are welded to the flanges of the column by full-penetration butt welds. The webs are bolted to the beams and welded to the columns. The characteristic features of this type of connection are the backing bars at the bottom of the beam flange, and the cope-holes left open to facilitate the field welding of the beam flanges. Fractures occurred in the welds, in the beam flanges, and/or in the column flanges, sometimes penetrating into the webs.Once the problem was discovered several large research projects were initiated at various university laboratories, such as The University of California at San Diego, the University of Washington in Seattle, the University of Texas at Austin, Lehigh University at Bethlehem, Pennsylvania, and at other places. The US Government under the leadership of the Federal Emergency Management Agency (FEMA) instituted a major national research effort. The needed work was deemed so extensivethat no single research agency could hope to cope with it. Consequently three California groups formed a consortium which manages the work:(1) Structural Engineering Association of California.(2) Applied Technology Council.(3) California Universities for Research in Earthquake Engineering.The first letters in the name of each agency were combined to form the acronym SAC, which is the name of the joint venture that manages the research. We shall read much from this agency as the results of the massive amounts of research performed under its aegis are being published in the next few years.The goals of the program are to develop reliable, practical and cost-effective guidelines for the identification and inspection of at-risk steel moment frame buildings, the repair or upgrading of damaged buildings, the design of new construction, and the rehabilitation of undamaged buildings.~ As can be seen, the scope far exceeds the narrow look at the connections only. The first phase of the research was completed at the end of 1996, and its main aim was to arrive at interim guidelines so that design work could proceed. It consisted of the following components:~ A state-of-the-art assessment of knowledge on steel connections.~ A survey of building damage.~ The evaluation of ground motion.~ Detailed building analyses and case studies.~ A preliminary experimental program.~ Professional training and quality assurance programs.~ Publishing of the Interim Design Guidelines.A number of reports were issued in this first phase of the work. A partial list of these is appended at the end of this paper.During the first phase of the SAC project a series of full-scale connection tests under static and, occasionally, dynamic cyclic tests were performed. Tests were of pre-Northridge-type connections (that is, connections as they existed at the time of the earthquake), of repaired and upgraded details, and of new recommendedconnection details. A schematic view of the testing program is illustrated in Fig.2.2.2 Some recommended strategies for new design are schematically shown in Fig. 2.2.3.Fig. 2.2.3 some recommended improvements in the interim guidelinesThe following possible causes, and their combinations, were found to have contributed to tile connection failures:~ Inadequate workmanship in the field welds.~ Insufficient notch-toughness of the weld metal.~ Stress raisers caused by the backing bars.~ Lack of complete fusion near the backing bar.~ Weld bead sizes were too big.~ Slag inclusion in the welds.While many of the failures can be directly attributed to the welding and thematerial of the joints, there are more serious questions relative to the structural system that had evolved over the years mainly based on economic considerations.' The structural system used relatively few rigid-frames of heavy members that were designed to absorb the seismic forces for large parts of the structure. These few lateral-force resistant frames provide insufficient redundancy. More rigid-frames with smaller members could have provided a tougher and more ductile structural system. There is a question of size effect: Test results from joints of smaller members were extrapolated to joints with larger members without adequate test verification. The effect of a large initial pulse may have triggered dynamic forces that could have caused brittle fracture in joints with fracture critical details and materials. Furthermore, the yield stress of the beams was about 30% to 40% larger than the minimum specified values assumed in design, and so the connection failed before the beams, which were supposed to form plastic hinges.As can be seen, there are many possible reasons for this massive failure rate, and there is blame to go around for everyone. No doubt, the discussion about why and how the joints failed will go on for many more years. The structural system just did not measure up to demands that were more severe than expected. What should be kept in mind, however, is that no structure collapsed or caused even superficial nonstructural damage, and no person was injured or killed. In the strictest sense the structure sacrificed itself so that no physical harm was done to its users. The economic harm, of course, was enormous.7. Future directions of structural steel research and conclusionThe future holds many challenges for structural steel research. The ongoing work necessitated by the two recent earthquakes that most affected conventional design methods, namely, the Northridge earthquake in the US and the Kobe earthquake in Japan, will continue well into the first decade of the next Century. It is very likely that future disasters of this type will bring yet other problems to the steel research community. There is a profound change in the philosophy of design for disasters: We can no longer be content with saving lives only, but we must also design structures which will not be so damaged as to require extensive repairs.Another major challenge will be the emergence of many new materials such as high-performance concrete and plastic composite structures. Steel structures will continually have to face the problem of having to demonstrate viability in the marketplace. This can only be accomplished by more innovative research. Furthermore, the new comprehensive limit-states design codes which are being implemented worldwide, need research to back up the assumptions used in the theories.Specifically, the following list highlights some of the needed research in steel structures:Systems reliability tools have been developed to a high degree of sophistication. These tools should be applied to the studies of bridge and building structures to define the optimal locations of monitoring instruments, to assess the condition and the remaining life of structures, and to intelligently design economic repair and retrofit operations.New developments in instrumentation, data transfer and large-scale computation will enable researchers to know more about the response of structures under severe actions, so that a better understanding of "real-life" behavior can be achieved.The state of knowledge about the strength of structures is well above the knowledge about serviceability and durability. Research is needed on detecting and preventing damage in service and from deterioration.The areas of fatigue and fracture mechanics on the one hand, and the fields of structural stability on the other hand, should converge into a more Unified conceptual entity.The problems resulting from the combination of inelastic stability and low-cycle fatigue in connections subject to severe cyclic loads due to seismic action will need to be solved.The performance of members, connections and connectors (e.g., shear connectors) under severe cyclic and dynamic loading requires extensive new research, including shakedown behavior.The list could go on, but one should never be too dogmatic about the future ofsuch a highly creative activity as research. Nature, society and economics will provide sufficient challenges for the future generation of structural engineers.近期美国在钢结构和钢筋混凝土结构研究和设计方面的发展这篇文章将总结对钢结构的研究展望.1.钢结构桥梁的研究美国国家运输和公路官员协会(AASTH0)是为美国桥梁发布设计标准的权威。
桥梁工程毕业论文英文Title: Analysis and Design of Bridge StructuresAbstract:Bridge engineering is an integral part of civil engineering and plays a crucial role in connecting communities and facilitating transportation. The purpose of this thesis is to analyze and design bridge structures, focusing on key components such as foundations, superstructures, and substructures. The analysis includes evaluating the structural behavior and load carrying capacity through the utilization of various analytical tools. Furthermore, the design phase encompasses selecting suitable materials and designing components to meet safety and durability requirements. The study serves as a comprehensive guide to understanding the principles and processes involved in bridge engineering.1. IntroductionBridges are vital infrastructure that connects people, places, and economies. The study of bridge engineering involves the application of core principles like physics, materials science, and mathematics todesign and construct safe and efficient bridge structures. This thesis aims to provide an overview of the analysis and design principles involved in bridge engineering.2. Structural AnalysisThe analysis of bridge structures is crucial to ensure their safety and functionality. This chapter presents various analytical techniques for evaluating bridge behavior. The use of finite element analysis, structural modeling, and computer-aided design software is discussed in detail. Different load types and load combinations are also considered to determine the resilience and load carrying capacity of the bridge.3. Foundation DesignThe foundation is a critical component of any bridge structure, as it transfers the loads from the superstructure to the underlying ground. This chapter explores various foundation types, such as shallow foundations, deep foundations, and pile foundations. Design considerations, including soil mechanics, bearing capacity, settlement analysis, and groundwater conditions, are discussed. The use ofgeotechnical engineering software to simulate and optimize foundation design is also explored.4. Superstructure DesignThe superstructure refers to the portion of the bridge that supports the traffic loads and transfers them to the substructure. This chapter discusses the different types of superstructures, including beam bridges, truss bridges, and arch bridges. The selection of materials, such as concrete, steel, and composite materials, is analyzed based on their structural properties and cost-effectiveness. The design process incorporates the calculation of load distribution, structural stability, and deflection limits.5. Substructure DesignThe substructure comprises the bridge piers, abutments, and retaining walls, which provide support to the superstructure. This chapter focuses on the design considerations for substructures, including the selection of suitable materials, analysis of load distribution, and evaluation of stability against various forces and environmental conditions. Design principles for reinforced concrete and masonry substructures are explored, along with mitigationstrategies for potential issues such as scour and seismic activity.6. Safety and DurabilityEnsuring safety and durability is of utmost importance in bridge engineering. This chapter discusses the necessary steps for evaluating the safety of bridge structures, including factor of safety calculations, failure mode analysis, and risk assessment procedures. The discussion also includes guidelines for maintenance and inspection to ensure long-term performance and durability.7. ConclusionThis thesis provides an in-depth analysis and design framework for bridge structures. By comprehensively exploring the key components of bridges, including foundations, superstructures, and substructures, it provides valuable insights into the principles and processes involved in bridge engineering. The knowledge gained from this study will contribute to the safe and efficient design and construction of future bridge projects.。
桥梁设计外文翻译文献桥梁设计外文翻译文献(文档含中英文对照即英文原文和中文翻译) 原文:A Bridge For All CenturiesAn extremely long-and record setting-main span was designed for the second bridge to across the Panama Canal in order to meet the owner’s requirement that no piers be placed in the water.Because no disruption of canal traffic was permitted at any time,the cable-stayed bridge of cast-in-place cancrete was carefully constructed using the balanced-cantilever method.In 1962 ,the Bridge of Americas(Puente de las America) opened to traffic,serving as the only fixed link across the Panama Canal .The bridge was designed to carry 60,000 vehicles per day on four lanes, but it has beenoperating above its capacity for many years.Toalleviate bottlenecks on the route that the bridge carries over the canal-the Pan-AmericanHighway(Inter-American Highway)-and promotegrowth on the western side of Panama,the country’s Ministry of Public Works(Ministerio de Obras Publicas,or MOP )decided to build a new highway systerm linking the northern part of Panama City,on the eastern side of the canal, to the town of Arraijan,located on the western side of the canal.The Centennial Bridge –named to commemorate 100 years of Panamanian independence-has noe been constructed and, when opend, will carry six lanes of traffic. This cable-stayed bridge of cast-in-place cancrete features a main span of 420m,the longest such span for this type of bridge in the Western Hemisphere.In 200 the MOP invited international bridge design firms to compete for the design of the crossing, requesting a two-package proposal:one techinical, the other financial. A total of eight proposals were received by December 2000 from established bridge design firms all over the world. After short-listing three firms on the basis of the technical merits of their proposals, the MOP selected T.Y.Lin International, of San Francisco, to prepare the bridge design and provide field construction support based on the firm’s financial package.The Centennial Bridge desige process was unique and aggressive,incorporating concepts from the traditional design/build/bid method, the design/build method , and the sa-called fast-track design process.T o complete the construction on time-that is ,within just 27 months-the design of the bridge was carried out to a level of 30 percent before construction bidding began, in December 2001.The selected contractor-the Wiesbaden,Germany,office of Bilfinger Berger,AG-was brought on board immediately after being selected by the MOP ,just as would be the case in a fast-track approach. The desige of the bridge was then completed in conjunction with construction , a process that id similan to desige/build.The design selected by the client features two single-mast towers,each supporting two sets of stay cables that align in one vertical plane.Concrete was used to construct both the towers and the box girder deck,as well as the approach structures.The MOP , in conjunction with the Panama Canal Authority,established the following requirements for the bridge design :A 420m,the minimum length for the main span to accommodate the recently widened Gaillard Cut,a narrow portion of the canal crossing the Continental Divide that was straightened and widened to 275m in 2002;A navigational envelope consisting of 80m of vertical clearance and 70mof horizontal clearance to accommodate the safe passage of a crane of World War 11 vintage-a gift from the /doc/e5324711c381e53a580216fc700abb 68a982ad21.html ernment that is used by the Panama Canal Authority to maintain the canal gates and facilities;A roadway wide enough to carry six lanes of traffic, three in each direction;A deck able to accommodate a 1.5m wide pedestrian walkway;A design that would adhere to the American Association of State Highway and Transportation Official standard for a 100-year service life and offer HS-25 truck loading;A structure that could carry two 0.6m dianeter water lines;A construction method that would not cross the canal at any time or interrupt canal operationa in any way.Because of the bridge’s long main span and the potential for strong seismic activity in the area,no single building code covered all aspects of the project.Therefore the team from T.Y. Lin International determinded which portions of several standard bridge specifications were applicable and which were not.The following design codes were used in developing the design criteria for the bridge,it is standard specifications for highway bridge ,16th ed,1996It was paramount that the towers of the cable-stayed structucture be erected on land to avoid potential ship collision and the need to construct expensive deep foundation in water. However, geological maps and boring logs produced during the preliminary design phrase revealed that the east and west banksof the canal, where the towers were to be located, featured vastly different geologicaland soil conditions. On the east side of the canal, beneath shallow layers of overburden that rangs in consistency from soft to hard, lies a block of basalt ranging from medium hard to hard with very closely spaced joint.The engineers determined that the basalt would provide a competent platform for the construction of shallow foundation for tower, piers, and approach structures on this side of bridge.The west side, however,featured the infamous Cucaracha Formation, which is a heterogeneous conglomerate of clay shale with inclusions of sandstone, basalt,and ash that is prone to landslide. As a sudsurface stratum the Cucaracha Formation is quite stable,but it quickly erodes when exposed to the elements. The engineers determined that deep foundations would therefore be needed for the western approach structure,the west tower,and the western piers.Before a detailed design of the foundationa could be developed,a thorough analysis of the seismic hazards at the site was required,The design seismic load for the project was developed on the basis of a probabilistic seismic hazard assessment that considered the conditions at the site.Such an assessment establishes the return period for a given earthquake and the corresponding intensity of ground shaking in the horizontal directtion in terms of an acceleration response spectrum.The PSHA determined two dominant seismic sources: a subduction source zone associated with the North Panama Deformed Belt capable of producing a seimic event as strong as 7.7MW,and the Rio Gatun Fault, capable of producing an event as strong as 6.5MW.The 7.7MW NPDB event was used as the safety evluationearthquake,that is,the maximum earthquake that could strike without putting the bridge out of service.The damage to the bridge would be minor but would require some closures of the bridge.The 6.5MWRio Gatun Fault event was used as the foundational evaluation earthquake,a lower-level temblor that would cause minimal damage to the bridge and would not require closures.For the FEE load case,the SEE loading was scaled back by two-thirds.The FEE is assumed to have a peak acceleration of 0.21g and a return period of 500 years; the probability that it will be exceeded within 50 years is 10 pencent and within 100 years,18 persent.The SEE is assumed to have a peak acceleration of 1.33g and a return period of 2,500 years;the probability that it will be exceeded within 50 years is 2 pencent and within 100 years,4 persent.Because of uncertainty about the direction from which the seismic waves would approach the site, a single response spectrum-a curve showing the mathematically computed maximum response of a set of simple damped harmonic oscillators of different natural frequencies to a particular earthquake ground acceleration-was used to characterize mitions in two mutually orthogonal directions in the horizontal plane.To conduct a time-history analysis of the bridge’s multiple supports,a set of synthetic motions with three components-longitudinal,transverse,and vertical-was developd using an iterative technique.Recorded ground motions from an earthquake in Chile in 1985 were used as “seed”motions for the sythesis process.A time delay estimate-that is,an estimate of the time it would take for the motions generated by the SEEand FEE earthquakes to travel from one point to the next-was create using theassumed seismic wave velocity and the distance between the piers of the /doc/e5324711c381e53a580216fc700abb 68a982ad21.html ing an assumed was velocity of approximately 2.5km/s,a delay on the order of half a second to a secondis appropriate for a bridge 1 to 2km long.Soil-foundation interaction studies were performed to determine the stiffness of the soil and foundation as well as the seismic excitation measurement that would be used in the dynamic analyses.The studieswere conducted by means of soil-pile models using linear and nonlinear soil layera of varying depths.The equivalent pile lengths in the studies-that is, the lengths representing the portions of a given pile that would actually be affected by a given earthquake-induced ground motion-ranged from2to10m.In such a three-dimensional model,there are six ways in which the soil can resist the movement of the lpile because of its stiffness:throngh axial force in the three directions and through bending moments in three directions.Because the bridge site contains so many layers of varying soil types,each layer had to be represented by a different stiffness matrix and then analyzed.Once the above analyses were completed,the T.Y.Lin International engineers-taking into consideration the project requirements developedby the owener-evaluated several different concrete cable-stayed designs.A number of structural systems were investigated,the main variables,superstructure cross sections,and the varying support conditions described above.The requirement that the evevation of the deck be quite high strongly influenced the tower configuration.For the proposeddeck elevation of more than 80m,the most economical tower shapes included single-and dual-mast towers as well as “goa l post”towers-that is,a design in which the two masts would be linked to each other by crossbeams.Ultimately the engineers designd the bridge to be 34.3m wide with a 420mlong cable-stayd main span,two 200mlong side spans-one on each side of the main span-and approach structures at the ends of the side spans.On the east side there is one 46m long concrete approach structure,while on the west side there are three,measuring 60,60,and 66m,for a total bridge length of 1,052m.The side spans are supported by four piers,referred to,from west to east,as P1.P2,P3,and P4.The bridge deck is a continuous single-cell box girder from abutment to abutment; the expansion joints are located at the abutments only. Deck movements on the order of 400 mm are expected at these modular expansion joints Multidirectional pot bearings are used at the piers and at the abutments to accommodate these movements.The deck was fixed to the two towers to facilitate the balanced-cantilevermethod of construction and to provide torsional rigidity and lateral restraint to the deck.. Transverse live loads, seismic loads, and wind loads are proportionally distributed to the towers and the piers by the fixity of the deck to the towers and by reinforced-concrete shear keys located at the top of P1, P3, and P4. The deck is allowed to move longitudinally over the abutments and piers. The longitudinal, seismic, live, and temperature loads are absorbed by what is known as portal frame structural behavior, whereby the towers and the deck form a portal-much like the frame of a door in a building-that acts in proportion to therelative stiffness of the two towers.As previously mentioned, the presence of competent basalt on the east side of the site meant that shallow foundations could be used there; in particular, spread footings were designed for the east tower, the east approach structure, and the east abutment. The west tower, the west approach structure, and the western piers (P2 and P3), however, had to be founded deep within the Cucaracha Formation. A total of 48 cast-in-drilled-hole (CIDH) shafts with 2 m outer diameters and lengths ranging from 25 to 35 m were required. A moment curvature analysis was performed to determine the capacity of the shafts with different amounts of longitudinal steel rebar. The results were plotted against the demands, and on the basis of the results the amount of required longitudinal reinforcing steel was determined to be 1 percent of the amount of concrete used in the shafts. The distribution of the longitudinal reinforcing steel was established by following code requirements, with consideration also given to the limitations of constructing CIDH piles with the contractor’s preferred method, which is the water or slurry displacement method.A minimum amount of transverse steel had to be determined for use in the plastic regions of the shaft-that is, those at the top one-eighth of eighth of each shaft and within the shaft caps, which would absorb the highest seismic demands. Once this amount was determined, it was used as the minimum for areas of the shafts above their points of fixity where large lateral displacements were expected to occur. The locations of the transverse steel were then established by following code requirements and by considering the construction limitations of CIDH piles. The transverse steel was spiral shaped.Even though thief foundation designs differed, the towers themselves were designed to be identical. Each measures 185.5 m from the top of its pile cap and is designed as a hollow reinforced-concrete shaft with a truncated elliptical cross section (see figure opposite). Each tower’s width in plan varies along its height, narrowing uniformly from 9.5 m at the base of the tower to 6 m at the top. In the longitudinal direction, each pylon tapers from 9.5 m at the base to about 8 m right below the deck level, which is about 87 m above the tower base. Above the deck level the tower’s sections vary from 4.6 m just above the deck to 4.5 m at the top. Each tower was designed with a 2 by 4 m opening for pedestrian passage along the deck, a design challenge requiring careful detailing.The towers were designed in a accordance with the latest provisions of the ATC earthquake design manual mentioned previously (ATC-32). Owing to the portal frame action along the b ridge’s longitudinal axis, special seismic detailing was implemented in regions with the potential to develop plastic hinges in the event of seismic activity-specifically, just below the deck and above the footing. Special confining forces and alternating open stirrups-with 90 and 135 degree hooks-within the perimeter of the tower shaft.In the transverse direction, the tower behaves like a cantilever, requiring concrete-confining steel at its base. Special attention was needed at the joint between the tower and the deck because of the central-plane stay-cable arrangement, it was necessary to provide sufficient torsional stiffness and special detailing at the pier-to-deck intersection. This intersection is highly congested with vertical reinforcing steel, the closely spaced confining stirrups of the tower shaft, and the deck prestressing andreinforcement.The approach structures on either side of the main span are supported on hollow reinforced-concrete piers that measure 8.28 by 5 m in plan. The design and detailing of the piers are consistent with the latest versions of the ATC and AASHTO specifications for seismic design. Capacity design concepts were applied to the design of the piers. This approach required the use of seismic modeling with moment curvature elements to capture the inelastic behavior of elements during seismic excitation. Pushover analyses of the piers were performed to calculate the displacement capacity of the piers and to compare them with the deformations computed in the seismic time-history analyses. To ensure an adequate ductility of the piers-an essential feature of the capacity design approach-it was necessary to provide adequate concrete-confining steel at those locations within the pier bases where plastic hinges are expected to form.The deck of the cable-stayed main span is composed of single-cell box girders of cast-in-place concrete with internal, inclined steel struts and transverse posttensioned ribs, or stiffening beams, toward the tops. Each box girder segment is 4.5 m deep and 6 m long. To facilitate construction and enhance the bridge’s elegant design, similar sizes were used for the other bridge spans. An integral concrete overlay with a thickness of 350 mm was installed instead of an applied concrete overlay on the deck. In contrast to an applied overlay, the integral overlay was cast along with each segment during the deck erection. Diamond grinding equipment was used to obtain the desired surface profile and required smoothness. The minimum grinding depth was 5 mm.A total of 128 stay cables were used, the largest comprising83 monostrands. All cables with a length of more than 80 m were equipped at their lower ends with internal hydraulic dampers. Corrosion protection for the monostrands involved galvanization of the wires through hot dipping, a tight high-density polyethylene (HDPE) sheath extruded onto each strand, and a special type of petroleum wax that fills all of the voids between the wires.The stays are spaecd every 6 m and are arranged in a fan pattern.They are designed to be stressed from the tower only and are anchored in line with a continuous stiffening beam at the centerline of the deck.The deck anchorage system is actually a composite steel frame that encapsulates two continous steel plates that anchor the stays and transfer the stay forces in a continuous and repetitive system-via shear studs-throuthout the extent of the cable-supported deck (see figure above).A steel frame was designed to transfer the stays’horizontal forces to the box girders through concrete-embedded longitudinal steel plates and to transfer the boxes’ vertical forces directly through the internal steel struts.This innovative and elegant load transfer system made rapid construction of the concrete deck segments-in cycles of three to five days-possible.In addition to the geotechnical and seismic analyses,several structural analyses were performed to accurately capture the behavior of this complex bridge.For the service-load analysis,which includes live,temperature,and wind loads,the engineers used SAP2000, a computer program created and maintained by Computers &Structrures,Inc.(CSI), of Berkeley, California.This program was selected for its ability to easily model the service loads and to account for tridimensional effects.For correct SAP2000 modeling,it was necessary to define a set of initial stresses on the cables, deck, and tower elements to capture the state of the structure at the end of construction.For the calculation of those initial stresses, a series of iterations on the basic model were performed to obtain the stay forces in the structure that balance both the bridges’s self-weight and the superimposed dead loads. Once the correct cable stiffness and stress distribution were obtained, all subsequent service-load analyses were performed to account for the geometric stiffness and P-deltaeffects, which consider the magnitude of an applied load (P) versus the displacement(delta).The seismic analysis of the structure was conducted using the SADSAP structural analysis program, also a CSI product, based on the differences in seismic motions that will be experienced at the different piers based on their distance from one another.This sophisticated program has the capability to model inelastic behavior in that flexural plastic hinges can readily be simulated.Plastic hinge elements were modeled at varous locations along the structure where the results from a preliminary response spectrum analysis in SAP2000 indicated that inelastic behavior might be expected.The time-history records pertaining to the site were used in conjunction with the SADSAP model to botain a performace-based design of the piers and towers and to verifh the design of several deck stctions.As previously mentioned,the construction contractor was brought on board earl y in the process;the company’s bid of $93 million was accepted and the project was awarded in March 2002.To guarantee unimpeded canal traffic,the bridge had to be constructed without the use of the canal waters.To accomplish this, the cast-in-place main-pain superstructure was erected using the balanced-cantilever method.Form travelers were usedto accomplish this, and they were designed in such a way that they could be used as an integral part of the pier tables’falsework.After assembly on the ground, two 380 Mg form travelers were raised independently into the pier table casting position and connected to each other.After an initial learning period, the contractor was able to achieve a four-day cycle for the casting of the cantilevered deck segments, an achievement that greatly enhanced the ability of the team to construct the project on time.Once the side-span and mai-span closures were cast, the travelers had to be removed from locations adjacent to the towers rather than over water so as to avoid any influence on canal traffic.To save time, the towers approach structure, and piers were built simultaneously.The approach viaducts were designed and built using the span-by-span erection method by means of an underslung suupport truss.The east viaduct span was built first and the support truss was then removed and transferred to the west side so that it could be used to build the three spans of the west viaduct, one span at a time.The bridge construction was completeed in Auguse 2004 at a cost of approximately $2,780 per square meter.Its opening awaits the completion of the rest of the highway it serves.跨越世纪之桥1962年,横跨巴拿马运河的美国大桥作为仅有的固定连接开放交通车。
桥梁的快速修复——圣彼得堡一座旧木桥的更换工作在今年年初完成在俄罗斯的圣彼得堡,崛起的交通水平和发展要求促使一个旧的电车轨道桥被改造为一个斜拉桥。
新的Lazarevsky大桥横跨马来亚内芙卡,并与今年早些时候建成通车,取代了一座本来供有轨电车通行但是现在只供行人行走的旧木质桥。
这座桥坐落于彼得格勒区,并且沿着Pionerskaya和Sportivnaya街道将Krestovsky和Petrogradsky群岛连接了起来,这两者都是当地的交通枢纽。
它始建于1949年,当时被称为Koltovsky桥,相邻马来亚内芙卡河堤。
但在1952年,为了纪念传说中的俄罗斯海军上将米哈伊尔拉扎列夫,路堤及桥梁被易名为拉扎列夫海军上将路堤和Lazarevsky桥。
这座桥由VV Blazhevich工程师设计,最初桥有11跨,中央一个是单叶。
它最初是设计用于电车,并且是当时该市唯一的一座电车轨道桥。
总长度为141m,总宽度为11m,层面由金属和木质材料组成。
木材支柱支撑的码头建在钢管桩基础上。
但是在2002年时,电车轨道被关闭,从那时起,这座桥只供行人使用。
这座桥梁的位置就意味着它服务这座城市的西部——包括Krestovsky岛的彼得格勒区。
所有到Krestovsky岛的车辆都用主要这个岛的Krestovsky桥,这自然导致该桥大大超载。
由于Lazarevsky桥并没有承受车辆荷载,所以它不被认为是彼得格勒区的交通网络的一部分。
但是,Krestovsky岛上计划在victory 公园里兴建一个体育场,离海边仅有3公里,这意味着城市的其余部分需要一个可靠的连接方式。
当地政府认为解决这个问题最好的办法就是重建Lazarevsky 桥。
新桥的规模取决于现有交通水平,并且考虑到了该地区未来的发展。
据预测,到2025年,Lazarevsky桥的全年平均日交通量将上升至16000车次。
车流高峰发生在体育场馆举行重大赛事时,此时该桥须能在一小时内纾缓这个地段的交通。
本科毕业设计外文翻译大跨度桥梁1.悬索桥悬索桥是现行的跨径超过600m大桥的唯一解决方案,而且对跨径在300m以上的桥梁它也是被认为是一种很有竞争力的方案。
现在世界上最大跨径的桥梁是纽约的威拉查诺(Verrazano)海峡大桥,另一个是英国的塞温(Savern)大桥。
悬索桥的组成部分有:柔性,主塔,锚碇,吊索(挂索),桥面板和加劲桁架。
主缆是有一组平行的单根高强钢丝在现场扭在一起并绑扎成型的钢丝束组成的。
每根钢丝都是经过渡锌处理的,并且整个用保护层覆盖着。
所用的钢丝应该是冷拔钢丝而不是经过热处理的各种钢丝。
在进行主塔设计时应该特别注意其在美学上的要求。
主塔很高而且具有足够的柔性,使其每一座塔顶都可认为是与主缆铰接。
主缆的两端很安全的锚固在非常坚实的锚碇上。
吊索把桥面板上的荷载传递到主主缆上。
吊索也是有高强钢丝制成的而且通常是竖直的。
桥面板通常是有加劲钢板,肋或槽型板,横梁制成的异性结构。
提供一些加劲梁连接在其主塔之间,能够起到控制空气动力运动并限制桥面板局部倾角变化。
如果加劲系统不适当,由于风引起的竖向振动也许会导致结构倾斜,就像塔科玛(Tacoma)海峡大桥的悲剧性的破坏所表明的那样。
边跨与主跨的跨径比的变化范围是0.17~0.50。
在现有的采用加劲梁的桥梁上,当跨径高大1000米时跨径与桥梁的建筑高度之比为85与100之间。
现有的桥梁的跨径与桥面板宽度之比约为20~56。
桥梁结构的空气动力稳定性必须得通过对其模型的风洞试验及细部分析进行全面的研究。
2.斜拉桥体系在过去的十年间,斜拉桥得以广泛的应用,尤其实在欧洲,而在世界其它地区,应用相对少一些。
在现代桥梁工程中,斜拉桥体系的重新兴旺起来是由于欧洲(主要是德国)的桥梁工程师有一种趋势,即从因为战争而短缺的材料上获得最佳的结构性能。
斜拉桥是有按各向异性桥面板和由吊索支撑的连续梁构成的体系建造起来的,这些吊索是一些穿过或固定的位于主桥墩的索塔顶上的倾斜主缆。
Study on nonlinear analysis of a highly redundantcable-stayed bridge1.AbstractA comparison on nonlinear analysis of a highly redundant cable-stayed bridge is performed in the study. The initial shapes including geometry and prestress distribution of the bridge are determined by using a two-loop iteration method, i.e., an equilibrium iteration loop and a shape iteration loop. For the initial shape analysis a linear and a nonlinear computation procedure are set up. In the former all nonlinearities of cable-stayed bridges are disregarded, and the shape iteration is carried out without considering equilibrium. In the latter all nonlinearities of the bridges are taken into consideration and both the equilibrium and the shape iteration are carried out. Based on the convergent initial shapes determined by the different procedures, the natural frequencies and vibration modes are then examined in details. Numerical results show that a convergent initial shape can be found rapidly by the two-loop iteration method, a reasonable initial shape can be determined by using the linear computation procedure, and a lot of computation efforts can thus be saved. There are only small differences in geometry and prestress distribution between the results determined by linear and nonlinear computation procedures. However, for the analysis of natural frequency and vibration modes, significant differences in the fundamental frequencies and vibration modes will occur, and the nonlinearities of the cable-stayed bridge response appear only in the modes determined on basis of the initial shape found by the nonlinear computation.2. IntroductionRapid progress in the analysis and construction of cable-stayed bridges has been made over the last three decades. The progress is mainly due to developments in the fields of computer technology, high strength steel cables, orthotropic steel decks and construction technology. Since the first modern cable-stayed bridge was built in Sweden in 1955, their popularity has rapidly been increasing all over the world. Because of its aesthetic appeal, economic grounds and ease of erection, thecable-stayed bridge is considered as the most suitable construction type for spans ranging from 200 to about 1000 m. The world’s longest cable-stayed bridge today is the Tatara bridge across the Seto Inland Sea, linking the main islands Honshu and Shikoku in Japan. The Tatara cable-stayed bridge was opened in 1 May, 1999 and has a center span of 890m and a total length of 1480m. A cable-stayed bridge consists of three principal components, namely girders, towers and inclined cable stays. The girder is supported elastically at points along its length by inclined cable stays so that the girder can span a much longer distance without intermediate piers. The dead load and traffic load on the girders are transmitted to the towers by inclined cables. High tensile forces exist in cable-stays which induce high compression forces in towers and part of girders. The sources of nonlinearity in cable-stayed bridges mainly include the cable sag, beam-column and large deflection effects. Since high pretension force exists in inclined cables before live loads are applied, the initial geometry and theprestress of cable-stayed bridges depend on each other. They cannot be specified independently as for conventional steel or reinforced concrete bridges. Therefore the initial shape has to be determined correctly prior to analyzing the bridge. Only based on the correct initial shape a correct deflection and vibration analysis can be achieved. The purpose of this paper is to present a comparison on the nonlinear analysis of a highly redundant stiff cable-stayed bridge, in which the initial shape of the bridge will be determined iteratively by using both linear and nonlinear computation procedures. Based on the initial shapes evaluated, the vibration frequencies and modes of the bridge are examined.3. System equations3.1. General system equationWhen only nonlinearities in stiffness are taken into account, and the system mass and damping matrices are considered as constant, the general system equation of a finite element model of structures in nonlinear dynamics can be derived from the Lagrange’s virtual work principle and written as follows:K j bαj-∑S j a jα= Mαβqβ”+ Dαβqβ’3.2. Linearized system equationIn order to incrementally solve the large deflection problem, the linearized system equations has to be derived. By taking the first order terms of the Taylor’s expansion of the general system equation, the linearized equation for a small time (or load) interval is obtained as follows:MαβΔqβ”+ΔDαβqβ’ +2KαβΔqβ=Δpα- u pα3.3. Linearized system equation in staticsIn nonlinear statics, the linearized system equation becomes2KαβΔqβ=Δpα- u pα4. Nonlinear analysis4.1. Initial shape analysisThe initial shape of a cable-stayed bridge provides the geometric configuration as well as the prestress distribution of the bridge under action of dead loads of girders and towers and under pretension force in inclined cable stays. The relations for the equilibrium conditions, the specified boundary conditions, and the requirements of architectural design should be satisfied. For shape finding computations, only the dead load of girders and towers is taken into account, and the dead load of cables is neglected, but cable sag nonlinearity is included. The computation for shape finding is performed by using the two-loop iteration method, i.e., equilibrium iteration and shape iteration loop. This can start with an arbitrary small tension force in inclined cables. Based on a reference configuration (the architectural designed form), having no deflection and zero prestress in girders and towers, the equilibrium position of the cable-stayed bridges under dead load is first determined iteratively (equilibrium iteration). Although this first determined configuration satisfies the equilibrium conditions and the boundary conditions, the requirements of architectural design are, in general, not fulfilled. Since the bridge span is large and no pretension forces exist in inclined cables, quite large deflections and very large bending moments may appear in the girders and towers. Another iteration then has to be carried out in orderto reduce the deflection and to smooth the bending moments in the girder and finally to find the correct initial shape. Such an iteration procedure is named here the ‘shape iteration ’. For shape iteration, the element axial forces determined in the previous step will be taken as initial element forces for the next iteration, and a newequilibrium configuration under the action of dead load and such initial forces will be determined again. During shape iteration, several control points (nodes intersected by the girder and the cable) will be chosen for checking the convergence tolerance. In each shape iteration the ratio of the vertical displacement at control points to the main span length will be checked, i.e.,ε<|spanmain points control at nt displaceme vertical | The shape iteration will be repeated until the convergence tolerance ε, say 10-4, isachieved. When the convergence tolerance is reached, the computation will stop and the initial shape of the cable-stayed bridges is found. Numerical experiments show that the iteration converges monotonously and that all three nonlinearities have less influence on the final geometry of the initial shape. Only the cable sag effect is significant for cable forces determined in the initial shape analysis, and thebeam-column and large deflection effects become insignificant.The initial analysis can be performed in two different ways: a linear and anonlinear computation procedure. 1. Linear computation procedure: To find the equilibrium configuration of the bridge, all nonlinearities of cable stayed bridges are neglected and only the linear elastic cable, beam-column elements and linear constant coordinate transformation coefficients are used. The shape iteration is carried out without considering the equilibrium iteration. A reasonable convergent initial shape is found, and a lot of computation efforts can be saved.2. Nonlinear computation procedure: All nonlinearities of cable-stayed bridges are taken into consideration during the whole computation process. The nonlinear cable element with sag effect and the beam-column element including stability coefficients and nonlinear coordinate transformation coefficients are used. Both the shape iteration and the equilibrium iteration are carried out in the nonlinearcomputation. Newton –Raphson method is utilized here for equilibrium iteration.4.2. Static deflection analysisBased on the determined initial shape, the nonlinear static deflection analysis of cable-stayed bridges under live load can be performed incrementwise or iterationwise. It is well known that the load increment method leads to large numerical errors. The iteration method would be preferred for the nonlinear computation and a desired convergence tolerance can be achieved. Newton – Raphson iteration procedure is employed. For nonlinear analysis of large or complex structural systems, a ‘full ’iteration procedure (iteration performed for a single full load step) will often fail. An increment –iteration procedure is highly recommended, in which the load will be incremented, and the iteration will be carried out in each load step. The static deflection analysis of the cable stayed bridge will start from the initial shapedetermined by the shape finding procedure using a linear or nonlinear computation.The algorithm of the static deflection analysis of cable-stayed bridges is summarized in Section 4.4.2.4.3. Linearized vibration analysisWhen a structural system is stiff enough and the external excitation is not too intensive, the system may vibrate with small amplitude around a certain nonlinear static state, where the change of the nonlinear static state induced by the vibration is very small and negligible. Such vibration with small amplitude around a certain nonlinear static state is termed linearized vibration. The linearized vibration is different from the linear vibration, where the system vibrates with small amplitude around a linear static state. The nonlinear static state qαa can be statically determined by nonlinear deflection analysis. After determining qαa , the system matrices may be established with respect to such a nonlinear static state, and the linearized system equation has the form as follows:MαβA qβ”+ DαβA qβ’+ 2KαβA qβ=pα(t)- TαAwhere the superscript ‘A’denotes the quantity calculated at the nonlinear static state a . This equation represents a set of linear ordinary differential equations of second qαorder with constant coefficient matrices MαβA, DαβA and 2KαβA. The equation can be solved by the modal superposition method, the integral transformation methods or the direct integration methods.When damping effect and load terms are neglected, the system equation becomesMαβA qβ” + 2KαβA qβ=0This equation represents the natural vibrations of an undamped system based on the nonlinear static state qαa The natural vibration frequencies and modes can be obtained from the above equation by using eigensolution procedures, e.g., subspace iteration methods. For the cable-stayed bridge, its initial shape is the nonlinear static state qαa . When the cable-stayed bridge vibrates with small amplitude based on the initial shape, the natural frequencies and modes can be found by solving the above equation.4.4. Computation algorithms of cable-stayed bridge analysisThe algorithms for shape finding computation, static deflection analysis and vibration analysis of cable-stayed bridges are briefly summarized in the following. 4.4.1. Initial shape analysis1. Input of the geometric and physical data of the bridge.2. Input of the dead load of girders and towers and suitably estimated initial forces in cable stays.3. Find equilibrium position(i) Linear procedure•Linear cable and beam-column stiffness elements are used.•Linear constant coordinate transformation coefficients a jαare used.by assembling element stiffness •Establish the linear system stiffness matrix Kαβmatrices.•Solve the linear system equation for qα(equilibrium position).•No equilibrium iteration is carried out.(ii) Nonlinear procedure•Nonlinear cables with sag effect and beam-column elements are used. •Nonlinear coordinate transformation coeffi- cients a jα; a jα,βare used..•Establish the tangent system stiffness matrix 2Kαβ•Solve the incremental system equation for △qα.•Equilibrium iteration is performed by using the Newton–Raphson method.4. Shape iteration5. Output of the initial shape including geometric shape and element forces.6. For linear static deflection analysis, only linear stiff-ness elements and transformation coefficients are used and no equilibrium iteration is carried out.4.4.3. Vibration analysis1. Input of the geometric and physical data of the bridge.2. Input of the initial shape data including initial geometry and initial element forces.3. Set up the linearized system equation of free vibrations based on the initial shape.4. Find vibration frequencies and modes by sub-space iteration methods, such as the Rutishauser Method.5. Estimation of the trial initial cable forcesIn the recent study of Wang and Lin, the shape finding of small cable-stayed bridges has been performed by using arbitrary small or large trial initial cable forces. There the iteration converges monotonously, and the convergent solutions have similar results, if different trial values of initial cable forces are used. However for large cable-stayed bridges, shape finding computations become more difficult to converge. In nonlinear analysis, the Newton-type iterative computation can converge, only when the estimated values of the solution is locate in the neighborhood of the true values. Difficulties in convergence may appear, when the shape finding analysis of cable-stayed bridges is started by use of arbitrary small initial cable forces suggested in the papers of Wang et al. Therefore, to estimate a suitable trial initial cable forces in order to get a convergent solution becomes important for the shape finding analysis. In the following, several methods to estimate trial initial cable forces will be discussed.5.1. Balance of vertical loads5.2. Zero moment control5.3. Zero displacement control5.4. Concept of cable equivalent modulus ratio5.5. Consideration of the unsymmetryIf the estimated initial cable forces are determined independently for each cable stay by the methods mentioned above, there may exist unbalanced horizontal forces on the tower in unsymmetric cable-stayed bridges. Forsymmetric arrangements of the cable-stays on the central (main) span and the side span with respect to the tower, the resultant of the horizontal components of the cable-stays acting on the tower is zero, i.e., no unbalanced horizontal forces exist on the tower. For unsymmetric cable-stayed bridges, in which the arrangement of cable-stays on the central (main) span and the side span is unsymmetric, and if the forces of cable stays on the central span and the side span are determined independently, evidently unbalanced horizontal forces willexist on the tower and will induce large bending moments and deflections therein. Therefore, for unsymmetric cable-stayed bridges, this problem can be overcome as follows. The force of cable stays on the central (main) span T i m can be determined by the methods mentioned above independently, where the superscript m denotes the main span, the subscript I denotes the ith cable stay. Then the force of cable stays on the side span is found by taking the equilibrium of horizontal force components at the node on the tower attached with the cable stays, i.e., T i m cosαi= T i s cosβi, and T i s = T i m cosαi/ cosβi, where αi is the angle between the ith cable stay and the girder on the main span, andβi, angle between the ith cable stay and the girder on the side span.6. ExamplesIn this study, two different types of small cable-stayed bridges are taken from literature, and their initial shapes will be determined by the previously described shape finding method using linear and nonlinear procedures. Finally, a highly redundant stiff cable-stayed bridge will be examined. A convergence tolerance e =10-4 is used for both the equilibrium iteration and the shape iteration. The maximum number of iteration cycles is set as 20. The computation is considered as not convergent, if the number of the iteration cycles exceeds 20.The initial shapes of the following two small cable stayed bridges in Sections 6.1 and 6.2 are first determined by using arbitrary trial initial cable forces. The iteration converges monotonously in these two examples. Their convergent initial shapes can be obtained easily without difficulties. There are only small differences between the initial shapes determined by the linear and the nonlinear computation. Convergent solutions offer similar results, and they are independent of the trial initial cable forces.7. ConclusionThe two-loop iteration with linear and nonlinear computation is established for finding the initial shapes of cable-stayed bridges. This method can achieve the architecturally designed form having uniform prestress distribution, and satisfies all equilibrium and boundary conditions. The determination of the initial shape is the most important work in the analysis of cable-stayed bridges. Only with a correct initial shape, a meaningful and accurate deflection and/or vibration analysis can be achieved. Based on numerical experiments in the study, some conclusions are summarized as follows:(1). No great difficulties appear in convergence of the shape finding of small cable-stayed bridges, where arbitrary initial trial cable forces can be used to start the computation. However for large scale cable-stayed bridges, serious difficulties occurred in convergence of iterations.(2). Difficulties often occur in convergence of the shape finding computation of large cable-stayed bridge, when trial initial cable forces are given by the methods of balance of vertical loads, zero moment control and zero displacement control. (3). A converged initial shape can be found rapidly by the two-loop iteration method, if the cable stress corresponding to about 80% of E eq=E value is used for the trial initial force of each cable stay in the main span, and the trial force of the cables in side spans is determined by taking horizontal equilibrium of the cable forces actingon the tower.(4). There are only small differences in geometry and prestress distributionforces. The iteration converges monotonously in these two examples. Their convergent initial shapes can be obtained easily without difficulties. There are only small differences between the initial shapes determined by the linear and the nonlinear computation. Convergent solutions offer similar results, and they are independent of the trial initial cable forces.7. ConclusionThe two-loop iteration with linear and nonlinear computation is established for finding the initial shapes of cable-stayed bridges. This method can achieve the architecturally designed form having uniform prestress distribution, and satisfies all equilibrium and boundary conditions. The determination of the initial shape is the most important work in the analysis of cable-stayed bridges. Only with a correct initial shape, a meaningful and accurate deflection and/or vibration analysis can be achieved. Based on numerical experiments in the study, some conclusions are summarized as follows:(1). No great difficulties appear in convergence of the shape finding of smallcable-stayed bridges, where arbitrary initial trial cable forces can be used to start the computation. However for large scale cable-stayed bridges, serious difficulties occurred in convergence of iterations.(2). Difficulties often occur in convergence of the shape finding computation of large cable-stayed bridge, when trial initial cable forces are given by the methods of balance of vertical loads, zero moment control and zero displacement control. (3). A converged initial shape can be found rapidly by the two-loop iteration method, if the cable stress corresponding to about 80% of E eq=E value is used for the trial initial force of each cable stay in the main span, and the trial force of the cablesin side spans is determined by taking horizontal equilibrium of the cable forces acting on the tower.(4). There are only small differences in geometry and prestress distribution between the results of initial shapes determined by linear and nonlinear procedures.(5). The shape finding using linear computation offers a reasonable initial shape and saves a lot of computation efforts, so that it is highly recommended from the point of view of engineering practices.(6). In small cable-stayed bridges, there are only small difference in the natural frequencies based on initial shapes determined by linear and nonlinear computation procedures, and the mode shapes are the same in both cases.(7). Significant differences in the fundamental frequency and in the mode shapes of highly redundant stiff cable stayed bridges is shown in the study. Only the vibration modes determined by the initial shape based on nonlinear procedures exhibit the nonlinear cable sag and beam-column effects of cable-stayed bridges, e.g., the first and third modes of the bridge are dominated by the transversal motion of the tower, not of the girder. The difference of the fundamental frequency in both cases is about 12%. Hence a correct analysis of vibration frequencies and modes of cable-stayed bridges can be obtained only when the ‘correct’initial shape is determined bynonlinear computation, not by the linear computation.高度超静定斜拉桥的非线性分析研究1.摘要一个拉索高度超静定的斜拉桥的非线性分析比较在研究中被实行。
桥梁工程中英文对照外文翻译文献(文档含英文原文和中文翻译)BRIDGE ENGINEERING AND AESTHETICSEvolvement of bridge Engineering,brief reviewAmong the early documented reviews of construction materials and structu re types are the books of Marcus Vitruvios Pollio in the first century B.C.The basic principles of statics were developed by the Greeks , and were exemplifi ed in works and applications by Leonardo da Vinci,Cardeno,and Galileo.In the fifteenth and sixteenth century, engineers seemed to be unaware of this record , and relied solely on experience and tradition for building bridges and aqueduc ts .The state of the art changed rapidly toward the end of the seventeenth cent ury when Leibnitz, Newton, and Bernoulli introduced mathematical formulatio ns. Published works by Lahire (1695)and Belidor (1792) about the theoretical a nalysis of structures provided the basis in the field of mechanics of materials .Kuzmanovic(1977) focuses on stone and wood as the first bridge-building materials. Iron was introduced during the transitional period from wood to steel .According to recent records , concrete was used in France as early as 1840 for a bridge 39 feet (12 m) long to span the Garoyne Canal at Grisoles, but r einforced concrete was not introduced in bridge construction until the beginnin g of this century . Prestressed concrete was first used in 1927.Stone bridges of the arch type (integrated superstructure and substructure) were constructed in Rome and other European cities in the middle ages . Thes e arches were half-circular , with flat arches beginning to dominate bridge wor k during the Renaissance period. This concept was markedly improved at the e nd of the eighteenth century and found structurally adequate to accommodate f uture railroad loads . In terms of analysis and use of materials , stone bridges have not changed much ,but the theoretical treatment was improved by introd ucing the pressure-line concept in the early 1670s(Lahire, 1695) . The arch the ory was documented in model tests where typical failure modes were considered (Frezier,1739).Culmann(1851) introduced the elastic center method for fixed-e nd arches, and showed that three redundant parameters can be found by the us e of three equations of coMPatibility.Wooden trusses were used in bridges during the sixteenth century when P alladio built triangular frames for bridge spans 10 feet long . This effort also f ocused on the three basic principles og bridge design : convenience(serviceabili ty) ,appearance , and endurance(strength) . several timber truss bridges were co nstructed in western Europe beginning in the 1750s with spans up to 200 feet (61m) supported on stone substructures .Significant progress was possible in t he United States and Russia during the nineteenth century ,prompted by the ne ed to cross major rivers and by an abundance of suitable timber . Favorable e conomic considerations included initial low cost and fast construction .The transition from wooden bridges to steel types probably did not begin until about 1840 ,although the first documented use of iron in bridges was the chain bridge built in 1734 across the Oder River in Prussia . The first truss completely made of iron was in 1840 in the United States , followed by Eng land in 1845 , Germany in 1853 , and Russia in 1857 . In 1840 , the first ir on arch truss bridge was built across the Erie Canal at Utica .The Impetus of AnalysisThe theory of structures ,developed mainly in the ninetheenth century,foc used on truss analysis, with the first book on bridges written in 1811. The Wa rren triangular truss was introduced in 1846 , supplemented by a method for c alculating the correcet forces .I-beams fabricated from plates became popular in England and were used in short-span bridges.In 1866, Culmann explained the principles of cantilever truss bridges, an d one year later the first cantilever bridge was built across the Main River in Hassfurt, Germany, with a center span of 425 feet (130m) . The first cantileve r bridge in the United States was built in 1875 across the Kentucky River.A most impressive railway cantilever bridge in the nineteenth century was the Fir st of Forth bridge , built between 1883 and 1893 , with span magnitudes of 1711 feet (521.5m).At about the same time , structural steel was introduced as a prime mater ial in bridge work , although its quality was often poor . Several early exampl es are the Eads bridge in St.Louis ; the Brooklyn bridge in New York ; and t he Glasgow bridge in Missouri , all completed between 1874 and 1883.Among the analytical and design progress to be mentioned are the contrib utions of Maxwell , particularly for certain statically indeterminate trusses ; the books by Cremona (1872) on graphical statics; the force method redefined by Mohr; and the works by Clapeyron who introduced the three-moment equation s.The Impetus of New MaterialsSince the beginning of the twentieth century , concrete has taken its place as one of the most useful and important structural materials . Because of the coMParative ease with which it can be molded into any desired shape , its st ructural uses are almost unlimited . Wherever Portland cement and suitable agg regates are available , it can replace other materials for certain types of structu res, such as bridge substructure and foundation elements .In addition , the introduction of reinforced concrete in multispan frames at the beginning of this century imposed new analytical requirements . Structures of a high order of redundancy could not be analyzed with the classical metho ds of the nineteenth century .The importance of joint rotation was already dem onstrated by Manderla (1880) and Bendixen (1914) , who developed relationshi ps between joint moments and angular rotations from which the unknown mom ents can be obtained ,the so called slope-deflection method .More simplification s in frame analysis were made possible by the work of Calisev (1923) , who used successive approximations to reduce the system of equations to one simpl e expression for each iteration step . This approach was further refined and int egrated by Cross (1930) in what is known as the method of moment distributi on .One of the most import important recent developments in the area of analytical procedures is the extension of design to cover the elastic-plastic range , also known as load factor or ultimate design. Plastic analysis was introduced with some practical observations by Tresca (1846) ; and was formulated by Sa int-Venant (1870) , The concept of plasticity attracted researchers and engineers after World War Ⅰ, mainly in Germany , with the center of activity shifting to England and the United States after World War Ⅱ.The probabilistic approa ch is a new design concept that is expected to replace the classical determinist ic methodology.A main step forward was the 1969 addition of the Federal Highway Adim inistration (F HWA)”Criteria for Reinforced Concrete Bridge Members “ that co vers strength and serviceability at ultimate design . This was prepared for use in conjunction with the 1969 American Association of State Highway Offficials (AASHO) Standard Specification, and was presented in a format that is readil y adaptable to the development of ultimate design specifications .According to this document , the proportioning of reinforced concrete members ( including c olumns ) may be limited by various stages of behavior : elastic , cracked , an d ultimate . Design axial loads , or design shears . Structural capacity is the r eaction phase , and all calculated modified strength values derived from theoret ical strengths are the capacity values , such as moment capacity ,axial load ca pacity ,or shear capacity .At serviceability states , investigations may also be n ecessary for deflections , maximum crack width , and fatigue .Bridge TypesA notable bridge type is the suspension bridge , with the first example bu ilt in the United States in 1796. Problems of dynamic stability were investigate d after the Tacoma bridge collapse , and this work led to significant theoretica l contributions Steinman ( 1929 ) summarizes about 250 suspension bridges bu ilt throughout the world between 1741 and 1928 .With the introduction of the interstate system and the need to provide stru ctures at grade separations , certain bridge types have taken a strong place in bridge practice. These include concrete superstructures (slab ,T-beams,concrete box girders ), steel beam and plate girders , steel box girders , composite const ruction , orthotropic plates , segmental construction , curved girders ,and cable-stayed bridges . Prefabricated members are given serious consideration , while interest in box sections remains strong .Bridge Appearance and AestheticsGrimm ( 1975 ) documents the first recorded legislative effort to control t he appearance of the built environment . This occurred in 1647 when the Cou ncil of New Amsterdam appointed three officials . In 1954 , the Supreme Cou rt of the United States held that it is within the power of the legislature to de termine that communities should be attractive as well as healthy , spacious as well as clean , and balanced as well as patrolled . The Environmental Policy Act of 1969 directs all agencies of the federal government to identify and dev elop methods and procedures to ensure that presently unquantified environmenta l amentities and values are given appropriate consideration in decision making along with economic and technical aspects .Although in many civil engineering works aesthetics has been practiced al most intuitively , particularly in the past , bridge engineers have not ignored o r neglected the aesthetic disciplines .Recent research on the subject appears to lead to a rationalized aesthetic design methodology (Grimm and Preiser , 1976 ) .Work has been done on the aesthetics of color ,light ,texture , shape , and proportions , as well as other perceptual modalities , and this direction is bot h theoretically and empirically oriented .Aesthetic control mechanisms are commonly integrated into the land-use re gulations and design standards . In addition to concern for aesthetics at the sta te level , federal concern focuses also on the effects of man-constructed enviro nment on human life , with guidelines and criteria directed toward improving quality and appearance in the design process . Good potential for the upgradin g of aesthetic quality in bridge superstructures and substructures can be seen in the evaluation structure types aimed at improving overall appearance .Lords and lording groupsThe loads to be considered in the design of substructures and bridge foun dations include loads and forces transmitted from the superstructure, and those acting directly on the substructure and foundation .AASHTO loads . Section 3 of AASHTO specifications summarizes the loa ds and forces to be considered in the design of bridges (superstructure and sub structure ) . Briefly , these are dead load ,live load , iMPact or dynamic effec t of live load , wind load , and other forces such as longitudinal forces , cent rifugal force ,thermal forces , earth pressure , buoyancy , shrinkage and long t erm creep , rib shortening , erection stresses , ice and current pressure , collisi on force , and earthquake stresses .Besides these conventional loads that are ge nerally quantified , AASHTO also recognizes indirect load effects such as fricti on at expansion bearings and stresses associated with differential settlement of bridge components .The LRFD specifications divide loads into two distinct cate gories : permanent and transient .Permanent loadsDead Load : this includes the weight DC of all bridge components , appu rtenances and utilities, wearing surface DW nd future overlays , and earth fill EV. Both AASHTO and LRFD specifications give tables summarizing the unit weights of materials commonly used in bridge work .Transient LoadsVehicular Live Load (LL) Vehicle loading for short-span bridges :considera ble effort has been made in the United States and Canada to develop a live lo ad model that can represent the highway loading more realistically than the H or the HS AASHTO models . The current AASHTO model is still the applica ble loading.桥梁工程和桥梁美学桥梁工程的发展概况早在公元前1世纪,Marcus Vitrucios Pollio 的著作中就有关于建筑材料和结构类型的记载和评述。
关于索桥英文作文高中英文:As a high school student, I have learned a lot aboutthe world around me, and one of the topics that has always fascinated me is the concept of suspension bridges. A suspension bridge, also known as a cable-stayed bridge, isa type of bridge that has cables supporting the bridge deck. These cables are attached to towers, which are usually located at the ends of the bridge.I find suspension bridges to be incredibly impressive because of their ability to span long distances and withstand the forces of nature. One example of a famous suspension bridge is the Golden Gate Bridge in San Francisco, which spans the Golden Gate Strait and is an iconic symbol of the city. The engineering and design ofthis bridge are truly remarkable, and it serves as a testament to human ingenuity and innovation.Another reason why I am interested in suspension bridges is because of their aesthetic appeal. The graceful curves and lines of a suspension bridge can be truly breathtaking, especially when seen against a backdrop of natural beauty. For example, the Akashi Kaikyo Bridge in Japan is not only a marvel of engineering, but also a stunning work of art that enhances the surrounding landscape.中文:作为一名高中学生,我对周围世界的了解越来越多,其中一个让我着迷的话题就是悬索桥的概念。
关于索桥英文作文初中作文英文:As a middle school student, I have learned a lot about the world around me. One of the most interesting things I have learned about is the concept of suspension bridges. A suspension bridge, also known as a cable-stayed bridge, is a type of bridge where the deck is hung below suspension cables on vertical suspenders. This design allows the bridge to span long distances and carry heavy loads.I remember learning about the famous Golden Gate Bridge in San Francisco, which is a prime example of a suspension bridge. The bridge is not only a vital transportation link, but also a symbol of the city. Its iconic red color and beautiful design make it a popular tourist attraction.Another famous suspension bridge is the Akashi Kaikyo Bridge in Japan. This bridge holds the record for the longest central span of any suspension bridge in the world.It is an engineering marvel and a testament to human ingenuity.I find suspension bridges fascinating because they combine beauty and functionality. The way they seem to float in the air and connect two points is truly amazing. It's like a work of art that also serves an important purpose.中文:作为一个中学生,我对周围的世界学到了很多。
有关吴江运河大桥的作文英文回答:The Wujiang Canal Bridge is an iconic landmark in Wujiang City, located in the Jiangsu Province of China. Itis a magnificent bridge that spans across the Wujiang River, connecting the two sides of the city. The bridge is notonly a transportation infrastructure but also a symbol of the city's development and progress.One of the reasons why the Wujiang Canal Bridge is so significant is its architectural design. The bridge is a cable-stayed bridge, which means that its main supporting cables are directly connected to the bridge towers. This design allows for a longer span and a more elegant appearance. The bridge towers are also beautifully designed, resembling pagodas, which adds a touch of cultural heritage to the modern structure.Another reason why the Wujiang Canal Bridge isimportant is its role in facilitating transportation. The bridge serves as a crucial link between the two sides of the city, allowing for the smooth flow of vehicles and pedestrians. This has greatly improved the connectivity and accessibility of the city, making it easier for people to travel and commute. As a result, the bridge has contributed to the economic development of the city by attracting more businesses and investments.Furthermore, the Wujiang Canal Bridge has become a popular tourist attraction in Wujiang City. Many visitors come to admire the bridge's grandeur and take photos of its stunning architecture. The bridge is especially beautiful at night when it is illuminated with colorful lights, creating a mesmerizing view. In addition, there are pedestrian walkways on the bridge, providing a unique experience for tourists to stroll along the river and enjoy the scenic surroundings.中文回答:吴江运河大桥是中国江苏省吴江市的一座标志性地标。
有关吴江运河大桥的作文英文回答:The Wujiang Canal Bridge is a magnificent structurethat spans the Wujiang Canal in Suzhou, Jiangsu Province, China. Constructed in 2002, it is a cable-stayed bridge with a total length of 1,203 meters and a main span of 450 meters, making it one of the longest bridges of its type in China.The bridge is designed in a modern and aesthetically pleasing style, with two large pylons supporting a network of cables that hold up the deck. The cables are arranged in a semi-harp configuration, giving the bridge a unique and striking appearance. The bridge deck is made of concrete and is supported by crossbeams that connect to the cables.The Wujiang Canal Bridge is an important transportation link in Suzhou, providing a convenient and efficient connection between the northern and southern parts of thecity. It is also a popular tourist destination, with many people visiting to admire its architectural beauty and to take in the panoramic views of the city from the bridge.The bridge is not only a transportation hub but also a symbol of Suzhou's economic development and progress. It is a reminder of the city's rich history and its continued growth and prosperity.中文回答:吴江运河大桥。
写桥梁的英文作文英文:Bridges are fascinating structures that connect people and places. They serve as important transportation links, allowing us to cross over rivers, valleys, and other obstacles. As a civil engineer, I have had the opportunity to design and build several bridges throughout my career.One of the most important considerations when designing a bridge is the type of material to use. There are many options, including wood, steel, concrete, and even stone. Each material has its own advantages and disadvantages, and the choice will depend on factors such as the location, the budget, and the expected lifespan of the bridge.Another important aspect of bridge design is the type of bridge to use. There are several types, including beam bridges, arch bridges, suspension bridges, and cable-stayed bridges. Each type has its own unique characteristics andis suited for different situations. For example, a suspension bridge is ideal for spanning long distances, while an arch bridge is better suited for shorter spans.In addition to the technical aspects of bridge design, there are also social and cultural considerations to take into account. Bridges can be iconic structures that represent a city or a region, and they can also have a significant impact on the local environment and community. For example, a bridge that is designed to blend in with the surrounding landscape may be more aesthetically pleasing and less disruptive to the local ecosystem.Overall, designing and building bridges is a challenging and rewarding profession. It requires a combination of technical knowledge, creativity, and a deep understanding of the needs and desires of the community.中文:桥梁是连接人与地方的迷人结构。
毕业设计(文献翻译)译文及原文复印件学生姓名:左烨学号: 1804070233 所在学院:交通学院专业:交通工程文献题目: Bridges桥梁类型指导教师:罗韧南京工业大学土木工程学院交通工程系二O一一年三月桥梁类型梁桥梁桥也许是最普遍也是最基本的桥梁结构形式。
一根木头跨越小河是典型梁桥的一种最简单的实例。
在现代的钢梁桥结构形式中,最常见的两种型式是I 型梁桥和箱梁。
如果我们考察I型梁的横截面我们马上就能理解为什么它被冠以如此的名字(见插图1)。
梁的横断面采用了英文字母I大写的形状。
中间的垂直板被称为肋板,而顶部和底部的平面板指的就是凸缘。
要解释I型梁为什么是一种有效的截面型式是一项长期而艰巨的任务,因此在本篇文章中我们就不做解释了。
箱梁得名如同于I型梁一样,很明显,它的截面形状类似于一个箱子。
典型的箱梁截面型式有两个肋板和两个凸缘(见插图2)。
但是在某些情况下,两个以上的肋板就会形成存在剪力滞现象的多室箱梁。
其他梁桥的例子包括π型梁——因其截面类似于数学符号π而得名,还有T 型梁。
因为绝大部分现今建造的梁桥都属于箱梁或是I型梁,所以我们会跳过这些少见的截面类型。
现在我们了解了I型梁和箱梁之间的外形差异,让我们来看看这两种截面型式的优缺点。
I型梁截面设计和建造简单,在大部分情况下,使用效果也很好。
但是,如果梁桥有任何形式的弯曲,梁就会受扭,也就是众所周知的扭矩。
对比于I型梁,在箱梁中添加的第二个肋板增加了稳定性,也就增加了箱梁的抗扭性能。
这就使得箱梁截面成为存在显著曲线梁桥的理想选择。
箱梁结构更稳定可以跨越更长的距离且经常用于大跨径桥梁,而使用I型梁就不会有足够的强度和稳定性。
然而,设计构造箱梁桥相比于I型梁更为困难。
例如,为了焊接箱型梁内的接缝,人工或是机械就必须能够控制箱梁产生的剪力滞。
桁架桥桁架是一种简单的类似于骨骼的结构。
在结构力学中,简单桁架的单个组成部分只受到拉力和压缩力,而不存在弯曲力。
斜交角度对钢筋混凝土板桥的影响C. Menassa1; M. Mabsout2; K. Tarhini3; and G. Frederick4摘要:本文提出用有限元法分析简单的跨度钢筋混凝土桥梁倾斜角的影响。
本文研究调查了跨距长度,板坯宽度和倾斜角的参数。
把倾斜的桥梁有限元分析(FEA)的结果进行了比较,参考直桥以及美国协会为国家公路和运输制定的AASHTO标准规范和LRFD程序。
共对96个桥梁进行了分析,并进行位置靠近一个边缘上的每一座桥产生了最大弯曲的板AASHTO HS-20设计的卡车的受力分析。
AASHTO标准规格的分析得到类似的结果到FEA最大纵弯矩为倾斜角小于或等于20°。
作为偏斜角增大,AASHTO标准规格20%高估的最大力矩为30°,50%为40°,和100%为50°。
AASHTO标准LRFD设计规范程序高估了FEA 最大纵向弯矩。
高估的数值随着斜交角的增加而增加,并且降低了通道的数目增加; AASHTO LRFD由偏斜角小于30°,达到50°50%至最高达40%的高估了纵弯矩。
用于偏斜和直桥在三维有限元纵向矩之间的比率几乎是一个用于与偏斜角小于20°的桥梁。
这个比例30和40°之间下降到0.75,如果桥的斜交角增加至50°,进一步降低至0.5。
这种减少在纵向力矩比通过在最大横向力矩比从0到50°的倾斜角的增大增加了高达75%的偏移。
对于偏斜桥梁和直桥梁FEA最大活载荷挠度之间的比在与该纵向时刻的一致的图形而减小。
这个比率当从一个偏斜角小于10°时,以0.6为40°和50°之间的斜交角减小。
DOI: 10.1061/ASCE1084-0702200712:2205关键词:桥梁,歪斜;混凝土板;有限元法;桥梁,高速公路;钢筋混凝土。
简介倾斜的桥梁在公路设计时经常遇到不能与直桥相连接的问题。
关于桥梁的作文English Answer:Bridges are majestic structures that connect people, communities, and nations. They traverse geographicalbarriers and symbolize the human ability to overcome challenges and achieve progress. Their significance extends beyond their functionality, as they often become iconic landmarks that embody architectural ingenuity and cultural heritage.The history of bridges dates back centuries, with the earliest known examples being simple log crossings andstone arches. As civilizations advanced, so did the complexity and sophistication of bridge designs. The Romans were renowned for their advanced bridge-building techniques, constructing impressive structures that spanned rivers and valleys. The Middle Ages saw the rise of medieval stone bridges, many of which still stand today as testaments tothe skill and craftsmanship of their builders.In the modern era, technological advancements have revolutionized bridge design and construction. Steel and concrete have become the materials of choice, allowing for the creation of longer and more complex spans. Suspension bridges, such as the Golden Gate Bridge in San Francisco, are marvels of engineering that push the boundaries of human ingenuity. Cable-stayed bridges, like the Brooklyn Bridge in New York City, are known for their elegant and efficient design.Bridges serve a variety of purposes, ranging from transportation and trade to social interaction and tourism. They facilitate the movement of goods, services, and people, stimulating economic growth and fostering cultural exchange. Bridges also provide access to remote areas, opening up new possibilities for exploration and development.Beyond their practical utility, bridges often hold symbolic and cultural significance. They represent connections not only between physical locations but also between communities, cultures, and generations. Iconicbridges like the Sydney Harbour Bridge and the Tower Bridge in London have become beloved landmarks, recognized around the world.In conclusion, bridges are remarkable feats of engineering that connect people, facilitate communication, and symbolize human progress. They are essential to the functioning of modern society and serve as enduring reminders of human ingenuity and determination.中文回答:桥梁在英文中称为bridge,是一种横跨自然或人造障碍物(如河流、峡谷或道路)的结构,允许人员或车辆安全通过。
Study on nonlinear analysis of a highly redundantcable-stayed bridge1.AbstractA comparison on nonlinear analysis of a highly redundant cable-stayed bridge is performed in the study. The initial shapes including geometry and prestress distribution of the bridge are determined by using a two-loop iteration method, i.e., an equilibrium iteration loop and a shape iteration loop. For the initial shape analysis a linear and a nonlinear computation procedure are set up. In the former all nonlinearities of cable-stayed bridges are disregarded, and the shape iteration is carried out without considering equilibrium. In the latter all nonlinearities of the bridges are taken into consideration and both the equilibrium and the shape iteration are carried out. Based on the convergent initial shapes determined by the different procedures, the natural frequencies and vibration modes are then examined in details. Numerical results show that a convergent initial shape can be found rapidly by the two-loop iteration method, a reasonable initial shape can be determined by using the linear computation procedure, and a lot of computation efforts can thus be saved. There are only small differences in geometry and prestress distribution between the results determined by linear and nonlinear computation procedures. However, for the analysis of natural frequency and vibration modes, significant differences in the fundamental frequencies and vibration modes will occur, and the nonlinearities of the cable-stayed bridge response appear only in the modes determined on basis of the initial shape found by the nonlinear computation.2. IntroductionRapid progress in the analysis and construction of cable-stayed bridges has been made over the last three decades. The progress is mainly due to developments in the fields of computer technology, high strength steel cables, orthotropic steel decks and construction technology. Since the first modern cable-stayed bridge was built in Sweden in 1955, their popularity has rapidly been increasing all over the world. Because of its aesthetic appeal, economic grounds and ease of erection, thecable-stayed bridge is considered as the most suitable construction type for spans ranging from 200 to about 1000 m. The world’s longest cable-stayed bridge today is the Tatara bridge across the Seto Inland Sea, linking the main islands Honshu and Shikoku in Japan. The Tatara cable-stayed bridge was opened in 1 May, 1999 and has a center span of 890m and a total length of 1480m. A cable-stayed bridge consists of three principal components, namely girders, towers and inclined cable stays. The girder is supported elastically at points along its length by inclined cable stays so that the girder can span a much longer distance without intermediate piers. The dead load and traffic load on the girders are transmitted to the towers by inclined cables. High tensile forces exist in cable-stays which induce high compression forces in towers and part of girders. The sources of nonlinearity in cable-stayed bridges mainly include the cable sag, beam-column and large deflection effects. Since high pretension force exists in inclined cables before live loads are applied, the initial geometry and theprestress of cable-stayed bridges depend on each other. They cannot be specified independently as for conventional steel or reinforced concrete bridges. Therefore the initial shape has to be determined correctly prior to analyzing the bridge. Only based on the correct initial shape a correct deflection and vibration analysis can be achieved. The purpose of this paper is to present a comparison on the nonlinear analysis of a highly redundant stiff cable-stayed bridge, in which the initial shape of the bridge will be determined iteratively by using both linear and nonlinear computation procedures. Based on the initial shapes evaluated, the vibration frequencies and modes of the bridge are examined.3. System equations3.1. General system equationWhen only nonlinearities in stiffness are taken into account, and the system mass and damping matrices are considered as constant, the general system equation of a finite element model of structures in nonlinear dynamics can be derived from the Lagrange’s virtual work principle and written as follows:K j bαj-∑S j a jα= Mαβqβ”+ Dαβqβ’3.2. Linearized system equationIn order to incrementally solve the large deflection problem, the linearized system equations has to be derived. By taking the first order terms of the Taylor’s expansion of the general system equation, the linearized equation for a small time (or load) interval is obtained as follows:MαβΔqβ”+ΔDαβqβ’ +2KαβΔqβ=Δpα- u pα3.3. Linearized system equation in staticsIn nonlinear statics, the linearized system equation becomes2KαβΔqβ=Δpα- u pα4. Nonlinear analysis4.1. Initial shape analysisThe initial shape of a cable-stayed bridge provides the geometric configuration as well as the prestress distribution of the bridge under action of dead loads of girders and towers and under pretension force in inclined cable stays. The relations for the equilibrium conditions, the specified boundary conditions, and the requirements of architectural design should be satisfied. For shape finding computations, only the dead load of girders and towers is taken into account, and the dead load of cables is neglected, but cable sag nonlinearity is included. The computation for shape finding is performed by using the two-loop iteration method, i.e., equilibrium iteration and shape iteration loop. This can start with an arbitrary small tension force in inclined cables. Based on a reference configuration (the architectural designed form), having no deflection and zero prestress in girders and towers, the equilibrium position of the cable-stayed bridges under dead load is first determined iteratively (equilibrium iteration). Although this first determined configuration satisfies the equilibrium conditions and the boundary conditions, the requirements of architectural design are, in general, not fulfilled. Since the bridge span is large and no pretension forces exist in inclined cables, quite large deflections and very large bending moments may appear in the girders and towers. Another iteration then has to be carried out in orderto reduce the deflection and to smooth the bending moments in the girder and finally to find the correct initial shape. Such an iteration procedure is named here the ‘shape iteration ’. For shape iteration, the element axial forces determined in the previous step will be taken as initial element forces for the next iteration, and a newequilibrium configuration under the action of dead load and such initial forces will be determined again. During shape iteration, several control points (nodes intersected by the girder and the cable) will be chosen for checking the convergence tolerance. In each shape iteration the ratio of the vertical displacement at control points to the main span length will be checked, i.e.,ε<|spanmain points control at nt displaceme vertical | The shape iteration will be repeated until the convergence tolerance ε, say 10-4, isachieved. When the convergence tolerance is reached, the computation will stop and the initial shape of the cable-stayed bridges is found. Numerical experiments show that the iteration converges monotonously and that all three nonlinearities have less influence on the final geometry of the initial shape. Only the cable sag effect is significant for cable forces determined in the initial shape analysis, and thebeam-column and large deflection effects become insignificant.The initial analysis can be performed in two different ways: a linear and anonlinear computation procedure. 1. Linear computation procedure: To find the equilibrium configuration of the bridge, all nonlinearities of cable stayed bridges are neglected and only the linear elastic cable, beam-column elements and linear constant coordinate transformation coefficients are used. The shape iteration is carried out without considering the equilibrium iteration. A reasonable convergent initial shape is found, and a lot of computation efforts can be saved.2. Nonlinear computation procedure: All nonlinearities of cable-stayed bridges are taken into consideration during the whole computation process. The nonlinear cable element with sag effect and the beam-column element including stability coefficients and nonlinear coordinate transformation coefficients are used. Both the shape iteration and the equilibrium iteration are carried out in the nonlinearcomputation. Newton –Raphson method is utilized here for equilibrium iteration.4.2. Static deflection analysisBased on the determined initial shape, the nonlinear static deflection analysis of cable-stayed bridges under live load can be performed incrementwise or iterationwise. It is well known that the load increment method leads to large numerical errors. The iteration method would be preferred for the nonlinear computation and a desired convergence tolerance can be achieved. Newton – Raphson iteration procedure is employed. For nonlinear analysis of large or complex structural systems, a ‘full ’iteration procedure (iteration performed for a single full load step) will often fail. An increment –iteration procedure is highly recommended, in which the load will be incremented, and the iteration will be carried out in each load step. The static deflection analysis of the cable stayed bridge will start from the initial shapedetermined by the shape finding procedure using a linear or nonlinear computation.The algorithm of the static deflection analysis of cable-stayed bridges is summarized in Section 4.4.2.4.3. Linearized vibration analysisWhen a structural system is stiff enough and the external excitation is not too intensive, the system may vibrate with small amplitude around a certain nonlinear static state, where the change of the nonlinear static state induced by the vibration is very small and negligible. Such vibration with small amplitude around a certain nonlinear static state is termed linearized vibration. The linearized vibration is different from the linear vibration, where the system vibrates with small amplitude around a linear static state. The nonlinear static state qαa can be statically determined by nonlinear deflection analysis. After determining qαa , the system matrices may be established with respect to such a nonlinear static state, and the linearized system equation has the form as follows:MαβA qβ”+ DαβA qβ’+ 2KαβA qβ=pα(t)- TαAwhere the superscript ‘A’denotes the quantity calculated at the nonlinear static state a . This equation represents a set of linear ordinary differential equations of second qαorder with constant coefficient matrices MαβA, DαβA and 2KαβA. The equation can be solved by the modal superposition method, the integral transformation methods or the direct integration methods.When damping effect and load terms are neglected, the system equation becomesMαβA qβ” + 2KαβA qβ=0This equation represents the natural vibrations of an undamped system based on the nonlinear static state qαa The natural vibration frequencies and modes can be obtained from the above equation by using eigensolution procedures, e.g., subspace iteration methods. For the cable-stayed bridge, its initial shape is the nonlinear static state qαa . When the cable-stayed bridge vibrates with small amplitude based on the initial shape, the natural frequencies and modes can be found by solving the above equation.4.4. Computation algorithms of cable-stayed bridge analysisThe algorithms for shape finding computation, static deflection analysis and vibration analysis of cable-stayed bridges are briefly summarized in the following. 4.4.1. Initial shape analysis1. Input of the geometric and physical data of the bridge.2. Input of the dead load of girders and towers and suitably estimated initial forces in cable stays.3. Find equilibrium position(i) Linear procedure•Linear cable and beam-column stiffness elements are used.•Linear constant coordinate transformation coefficients a jαare used.by assembling element stiffness •Establish the linear system stiffness matrix Kαβmatrices.•Solve the linear system equation for qα(equilibrium position).•No equilibrium iteration is carried out.(ii) Nonlinear procedure•Nonlinear cables with sag effect and beam-column elements are used. •Nonlinear coordinate transformation coeffi- cients a jα; a jα,βare used..•Establish the tangent system stiffness matrix 2Kαβ•Solve the incremental system equation for △qα.•Equilibrium iteration is performed by using the Newton–Raphson method.4. Shape iteration5. Output of the initial shape including geometric shape and element forces.6. For linear static deflection analysis, only linear stiff-ness elements and transformation coefficients are used and no equilibrium iteration is carried out.4.4.3. Vibration analysis1. Input of the geometric and physical data of the bridge.2. Input of the initial shape data including initial geometry and initial element forces.3. Set up the linearized system equation of free vibrations based on the initial shape.4. Find vibration frequencies and modes by sub-space iteration methods, such as the Rutishauser Method.5. Estimation of the trial initial cable forcesIn the recent study of Wang and Lin, the shape finding of small cable-stayed bridges has been performed by using arbitrary small or large trial initial cable forces. There the iteration converges monotonously, and the convergent solutions have similar results, if different trial values of initial cable forces are used. However for large cable-stayed bridges, shape finding computations become more difficult to converge. In nonlinear analysis, the Newton-type iterative computation can converge, only when the estimated values of the solution is locate in the neighborhood of the true values. Difficulties in convergence may appear, when the shape finding analysis of cable-stayed bridges is started by use of arbitrary small initial cable forces suggested in the papers of Wang et al. Therefore, to estimate a suitable trial initial cable forces in order to get a convergent solution becomes important for the shape finding analysis. In the following, several methods to estimate trial initial cable forces will be discussed.5.1. Balance of vertical loads5.2. Zero moment control5.3. Zero displacement control5.4. Concept of cable equivalent modulus ratio5.5. Consideration of the unsymmetryIf the estimated initial cable forces are determined independently for each cable stay by the methods mentioned above, there may exist unbalanced horizontal forces on the tower in unsymmetric cable-stayed bridges. Forsymmetric arrangements of the cable-stays on the central (main) span and the side span with respect to the tower, the resultant of the horizontal components of the cable-stays acting on the tower is zero, i.e., no unbalanced horizontal forces exist on the tower. For unsymmetric cable-stayed bridges, in which the arrangement of cable-stays on the central (main) span and the side span is unsymmetric, and if the forces of cable stays on the central span and the side span are determined independently, evidently unbalanced horizontal forces willexist on the tower and will induce large bending moments and deflections therein. Therefore, for unsymmetric cable-stayed bridges, this problem can be overcome as follows. The force of cable stays on the central (main) span T i m can be determined by the methods mentioned above independently, where the superscript m denotes the main span, the subscript I denotes the ith cable stay. Then the force of cable stays on the side span is found by taking the equilibrium of horizontal force components at the node on the tower attached with the cable stays, i.e., T i m cosαi= T i s cosβi, and T i s = T i m cosαi/ cosβi, where αi is the angle between the ith cable stay and the girder on the main span, andβi, angle between the ith cable stay and the girder on the side span.6. ExamplesIn this study, two different types of small cable-stayed bridges are taken from literature, and their initial shapes will be determined by the previously described shape finding method using linear and nonlinear procedures. Finally, a highly redundant stiff cable-stayed bridge will be examined. A convergence tolerance e =10-4 is used for both the equilibrium iteration and the shape iteration. The maximum number of iteration cycles is set as 20. The computation is considered as not convergent, if the number of the iteration cycles exceeds 20.The initial shapes of the following two small cable stayed bridges in Sections 6.1 and 6.2 are first determined by using arbitrary trial initial cable forces. The iteration converges monotonously in these two examples. Their convergent initial shapes can be obtained easily without difficulties. There are only small differences between the initial shapes determined by the linear and the nonlinear computation. Convergent solutions offer similar results, and they are independent of the trial initial cable forces.7. ConclusionThe two-loop iteration with linear and nonlinear computation is established for finding the initial shapes of cable-stayed bridges. This method can achieve the architecturally designed form having uniform prestress distribution, and satisfies all equilibrium and boundary conditions. The determination of the initial shape is the most important work in the analysis of cable-stayed bridges. Only with a correct initial shape, a meaningful and accurate deflection and/or vibration analysis can be achieved. Based on numerical experiments in the study, some conclusions are summarized as follows:(1). No great difficulties appear in convergence of the shape finding of small cable-stayed bridges, where arbitrary initial trial cable forces can be used to start the computation. However for large scale cable-stayed bridges, serious difficulties occurred in convergence of iterations.(2). Difficulties often occur in convergence of the shape finding computation of large cable-stayed bridge, when trial initial cable forces are given by the methods of balance of vertical loads, zero moment control and zero displacement control. (3). A converged initial shape can be found rapidly by the two-loop iteration method, if the cable stress corresponding to about 80% of E eq=E value is used for the trial initial force of each cable stay in the main span, and the trial force of the cables in side spans is determined by taking horizontal equilibrium of the cable forces actingon the tower.(4). There are only small differences in geometry and prestress distributionforces. The iteration converges monotonously in these two examples. Their convergent initial shapes can be obtained easily without difficulties. There are only small differences between the initial shapes determined by the linear and the nonlinear computation. Convergent solutions offer similar results, and they are independent of the trial initial cable forces.7. ConclusionThe two-loop iteration with linear and nonlinear computation is established for finding the initial shapes of cable-stayed bridges. This method can achieve the architecturally designed form having uniform prestress distribution, and satisfies all equilibrium and boundary conditions. The determination of the initial shape is the most important work in the analysis of cable-stayed bridges. Only with a correct initial shape, a meaningful and accurate deflection and/or vibration analysis can be achieved. Based on numerical experiments in the study, some conclusions are summarized as follows:(1). No great difficulties appear in convergence of the shape finding of smallcable-stayed bridges, where arbitrary initial trial cable forces can be used to start the computation. However for large scale cable-stayed bridges, serious difficulties occurred in convergence of iterations.(2). Difficulties often occur in convergence of the shape finding computation of large cable-stayed bridge, when trial initial cable forces are given by the methods of balance of vertical loads, zero moment control and zero displacement control. (3). A converged initial shape can be found rapidly by the two-loop iteration method, if the cable stress corresponding to about 80% of E eq=E value is used for the trial initial force of each cable stay in the main span, and the trial force of the cablesin side spans is determined by taking horizontal equilibrium of the cable forces acting on the tower.(4). There are only small differences in geometry and prestress distribution between the results of initial shapes determined by linear and nonlinear procedures.(5). The shape finding using linear computation offers a reasonable initial shape and saves a lot of computation efforts, so that it is highly recommended from the point of view of engineering practices.(6). In small cable-stayed bridges, there are only small difference in the natural frequencies based on initial shapes determined by linear and nonlinear computation procedures, and the mode shapes are the same in both cases.(7). Significant differences in the fundamental frequency and in the mode shapes of highly redundant stiff cable stayed bridges is shown in the study. Only the vibration modes determined by the initial shape based on nonlinear procedures exhibit the nonlinear cable sag and beam-column effects of cable-stayed bridges, e.g., the first and third modes of the bridge are dominated by the transversal motion of the tower, not of the girder. The difference of the fundamental frequency in both cases is about 12%. Hence a correct analysis of vibration frequencies and modes of cable-stayed bridges can be obtained only when the ‘correct’initial shape is determined bynonlinear computation, not by the linear computation.高度超静定斜拉桥的非线性分析研究1.摘要一个拉索高度超静定的斜拉桥的非线性分析比较在研究中被实行。